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Case Study Questions for Class 8 Maths

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Here in this article, we are providing case study questions for class 8 maths.

Maths Class 8 Chapter List

Latest chapter list (2023-24).

Chapter 1 Rational Numbers Chapter 2 Linear Equations in One Variable Chapter 3 Understanding Quadrilaterals Chapter 4 Data Handling Chapter 5 Squares and Square Roots Chapter 6 Cubes and Cube Roots Chapter 7 Comparing Quantities Chapter 8 Algebraic Expressions and Identities Chapter 9 Mensuration Chapter 10 Exponents and Powers Chapter 11 Direct and Indirect proportions Chapter 12 Factorisation Chapter 13 Introduction to Graphs

Old Chapter List

Chapter 1 Rational Numbers Chapter 2 Linear Equations in One Variable Chapter 3 Understanding Quadrilaterals Chapter 4 Practical Geometry Chapter 5 Data Handling Chapter 6 Squares and Square Roots Chapter 7 Cubes and Cube Roots Chapter 8 Comparing Quantities Chapter 9 Algebraic Expressions and Identities Chapter 10 Visualising Solid Shapes Chapter 11 Mensuration Chapter 12 Exponents and Powers Chapter 13 Direct and Indirect proportions Chapter 14 Factorisation Chapter 15 Introduction to Graphs Chapter 16 Playing with Numbers

Tips for Answering Case Study Questions for Class 8 Maths in Exam

1. Comprehensive Reading for Context: Prioritize a thorough understanding of the provided case study. Absorb the contextual details and data meticulously to establish a strong foundation for your solution.

2. Relevance Identification: Pinpoint pertinent mathematical concepts applicable to the case study. By doing so, you can streamline your thinking process and apply appropriate methods with precision.

3. Deconstruction of the Problem: Break down the complex problem into manageable components or steps. This approach enhances clarity and facilitates organized problem-solving.

4. Highlighting Key Data: Emphasize critical information and data supplied within the case study. This practice aids quick referencing during the problem-solving process.

5. Application of Formulas: Leverage pertinent mathematical formulas, theorems, and principles to solve the case study. Accuracy in formula selection and unit usage is paramount.

6. Transparent Workflow Display: Document your solution with transparency, showcasing intermediate calculations and steps taken. This not only helps track progress but also offers insight into your analytical process.

7. Variable Labeling and Definition: For introduced variables or unknowns, offer clear labels and definitions. This eliminates ambiguity and reinforces a structured solution approach.

8. Step Explanation: Accompany each step with an explanatory note. This reinforces your grasp of concepts and demonstrates effective application.

9. Realistic Application: When the case study pertains to real-world scenarios, infuse practical reasoning and logic into your solution. This ensures alignment with real-life implications.

10. Thorough Answer Review: Post-solving, meticulously review your answer for accuracy and coherence. Assess its compatibility with the case study’s context.

11. Solution Recap: Before submission, revisit your solution to guarantee comprehensive coverage of the problem and a well-organized response.

12. Previous Case Study Practice: Boost your confidence by practicing with past case study questions from exams or textbooks. This familiarity enhances your readiness for the question format.

13. Efficient Time Management: Strategically allocate time for each case study question based on its complexity and the overall exam duration.

14. Maintain Composure and Confidence: Approach questions with poise and self-assurance. Your preparation equips you to conquer the challenges presented.

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Important Questions Class 8 Maths Chapter 9

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Important Questions Class 8 Mathematics Chapter 9 – Algebraic Expressions and Identities

Algebra is one of the wide areas of Mathematics that studies mathematical expressions involving variables, constants, and mathematical operations like addition, subtraction, multiplication, and division. Algebra is the basis for higher mathematics studies in many fields, including science, engineering, medicine, and economics.

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Class 8 Mathematics Chapter 9 – Algebraic expressions and identities is the continuation of the earlier classes and chapters, where students learned about basic algebraic expressions like x + 3, 2y – 5, 3x², 4xy + 7 etc. Many more complex expressions can be formed using variables and constants. The topics covered in Chapter 9 are discussed in the points below.

Expressions: The problem statement is formed by combining variables, constants and mathematical operators.
Variables and constants: Consider the example 2x – 3. This expression is formed from the variable X and constants 2 and 3. With different values of the variable x, the result of the expression 2x – 3 changes.
Terms, factors, and coefficients: Terms in the expression are the product of its factors. The expression 2x – 3 is formed by two terms, 2x and 3. The term 2x is the product of its factors 2 and x. The term 3 comprises just one factor, i.e., 3.

A coefficient is the numerical factor of the term. In the expression 5xy + 3z, the coefficient of the term 5xy is 5, and the coefficient of the term 3z is 3.

Types of expressions: The three main types of algebraic expressions are,

Monomials: Expression formed with only one term. For example, 4x², -5z, 9xz², etc.

Binomials: Expression formed with two terms. For example 5x – 2, 6y – 9x², a + b, etc

Polynomials: A polynomial is an expression containing one or more terms with a non-zero coefficient and variables having non-negative integers as exponents. For example 2xy, 6x³ + 4x³ + 3x – 1, etc.

Like and unlike terms: Like terms have the same variables and exponents. However, the coefficients need not be the same. Unlike terms are two or more terms that do not have the same variables or exponents. The order of the variables does not matter unless there is power. To understand better, check the following examples of both types.

Like terms: 4b + 10b, 2x² + 4x², 15w – 13.4w, etc.

Unlike terms: 2x + 9y, 10a² – 9b, x³ – x², etc.

Subtraction and addition of algebraic expressions: While adding or subtracting polynomials, first add or subtract the like terms; and then handle the unlike terms.
Multiplication of algebraic expressions: There are three ways to multiply expressions:

(1) A monomial multiplied by a monomial,

(2) A polynomial multiplied by a monomial and

(3) A polynomial multiplied by a polynomial

Identity: An algebra identity is an equality, which means that the left-hand side of the equation is equal to the right-hand side for all values of the variables. Identities are very useful for solving equations in simple and easy steps. The four standard identities are,
(a + b)² = a² + 2ab + b²
(a – b)² = a² – 2ab + b²
(a + b) (a – b) = a² – b²
(x + a) (x + b) = x² + (a + b)x + ab

Algebra is an overwhelming and difficult chapter for many students, requiring critical thinking and creative problem-solving skills. Extramarks is one of the most trusted online learning platforms to help students understand the concepts clearly and prepare well for the examinations. Our highly experienced and expert Mathematics teachers have prepared CBSE Mathematics preparation materials for Class 8 students. These study resources include NCERT solutions, solved question papers, sample papers, CBSE revision notes, and more, per the CBSE syllabus and NCERT guidelines.

Get Access to CBSE Class 8 Maths Important Questions 2022-23 with Chapter-Wise Solutions

You can also find CBSE Class 8 Maths Chapter-by-Chapter Important Questions here:



1	Chapter 1
2	Chapter 2
3	Chapter 3
4	Chapter 4
5	Chapter 5
6	Chapter 6
7	Chapter 7
8	Chapter 8
9	Chapter 9	Algebraic Expressions and Identities
10	Chapter 10
11	Chapter 11
12	Chapter 12
13	Chapter 13
14	Chapter 14
15	Chapter 15
16	Chapter 16

Important Questions Class 8 Mathematics Chapter 9 – With Solutions

A complete list of Important Questions Class 8 Mathematics Chapter 9 provided on the Extramarks website consists of various questions for students to analyse their weak areas and practise until they thoroughly understand all the concepts and reduce mistakes. Chapter 9 Class 8 Mathematics Important Questions includes short answer questions, long answer questions, and MCQs backed with detailed and easy-to-understand solutions. These important questions are collated from the NCERT textbook and other genuine sources. By practising from solved question papers, sample papers, and the Mathematics Class 8 Chapter 9 Important Questions, students get familiar with the exam pattern and improve their time-management skills. Regular practise improves the calculating speed, which is helpful in the examination.

Register on the Extramarks website to refer to and practise the Important Questions Class 8 Mathematics Chapter 9 and other chapter-wise questions.

Below is a sample list of questions and their solutions from our Class 8 Mathematics Chapter 9 Important Questions:

Question 1. Find the terms and their coefficients for each of the following expressions.

(i) 5xyz² – 3zy

(ii) 1 + x+ x²

(iii) 4x²y² – 4x²y²z² + z²

(iv) 3- pq + qr – rp

(v) x/2 + y/2 – xy

(vi) 0.3a – 0.6ab + 0.5b

Answer 1. The terms and coefficients are given below,

Terms	Coefficient
(i) 5xyz², -3zy	5, -3
(ii) 1, x, x²	1, 1, 1
(iii) 4x²y², -4x²y²z², z²	4, -4, 1
(iv) 3, -pq, qr, -rp	3, -1, 1, -1
(v) x/2, y/2, -xy	1/2, 1/2, -1
(vi) 0.3a, -0.6ab, 0.5b	0.3, -0.6, 0.5

Question 2. Classify the following polynomials as monomials, binomials, and trinomials. Also, state the

polynomials do not fall in any of these three categories?

x + y, 1000, x + x² + x³, 7 + y + 5x, 2y – 3y², 2y – 3y² + 4y³, 5x – 4y + 3xy, 4z – 15z², ab + bc + cd + da, pqr,

p²q + pq², 2p + 2q,

Answer 2. The classified terms are given below,

Monomials- 1000, pqr

Binomials- x + y, 2y – 3y², 4z – 15z², p²q + pq², 2p + 2q

Trinomials- x + x²+ x³, 7 + y + 5x, 2y – 3y² + 4y³, 5x – 4y + 3xy

Polynomials that do not fall in any of these categories are x + y, x + x²+ x³, ab + bc + cd + da

Question 3. Add the following.

(i) ab – bc, bc – ca, ca – ab

(ii) a – b + ab, b – c + bc, c – a + ac

(iii) 2p²q² – 3pq + 4, 5 + 7pq – 3p²q²

(iv) l² + m², m² + n², n² + l², 2lm + 2mn + 2nl

Answer 3. (i) (ab – bc) + (bc – ca) + (ca – ab)

= ab – bc + bc – ca + ca – ab

= ab-ab-bc+bc-ca+ca

= 0

(ii) (a – b + ab) + (b – c + bc) + (c – a + ac)

= a – b + ab + b – c + bc + c -a +ac

= a – a -b + b + ab – c + c + bc + ac

= ab + bc + ac

(iii) ( 2p²q² – 3pq + 4) + ( 5 + 7pq – 3p²q²)

= 2p²q² – 3pq + 4 + 5 + 7pq – 3p²q²

= 2p²q² – 3p²q² + 7pq – 3pq + 4 + 5

= -1p²q² + 4pq + 9

= 4pq + 9 – p²q²

(iv) ( l² + m²) + (m² + n²) + (n² + l²) + (2lm + 2mn + 2nl)

= l² + m² + m² + n² + n² + l² + 2lm + 2mn + 2nl

= l² + l² + m² + m² + n² + n² + 2lm + 2mn + 2nl

= 2l² + 2m² + 2n² + 2lm + 2mn + 2nl

= 2( l² + m² + n² + lm + mn + nl)

Question 4. Subtract the following.

(i) 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3

(ii 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz

(iii) 4p²q – 3pq + 5pq²– 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq2+ 5p²q

(i) ( 12a – 9ab + 5b – 3 ) – ( 4a – 7ab + 3b + 12 )

= 12a – 9ab + 5b – 3 – 4a + 7ab – 3b – 12

= 12a – 4a – 9ab + 7ab + 5b –3b – 3 – 12

= 8a – 2ab + 2b – 15

(ii) ( 5xy – 2yz – 2zx + 10xyz ) – ( 3xy + 5yz – 7zx )

= 5xy – 2yz – 2zx + 10xyz – 3xy – 5yz + 7zx

= 5xy – 3xy – 2yz – 5yz – 2zx + 7zx + 10xyz

= 2xy – 7yz + 5zx + 10xyz

(iii) ( 18 – 3p – 11q + 5pq – 2pq2+ 5p²q ) – ( 4p²q – 3pq + 5pq²– 8p + 7q – 10 )

= 18 – 3p – 11q + 5pq – 2pq2 + 5p²q – 4p²q + 3pq – 5pq² + 8p – 7q + 10

= 18 + 10 – 3p + 8p – 11q – 7q + 5pq + 3pq – 2pq2 – 5pq² + 5p²q – 4p²q

= 28 + 5p – 18q + 8pq – 7pq² + p²q

Question 5. Multiply the following.

(i) – 7pq²r³, – 13p³q²r

(ii) 3x²y²z², 17xyz

(iii) 15xy², 17yz²

(iv) –5a²bc, 11ab, 13abc²

(v) (pq – 2r), (pq – 2r)

(vi) (3/2p² + 2/3q²), (2p² –3q²)

Answer 5. (i) ( – 7pq²r³ ) x ( – 13p³q²r )

= 91P 4 q 4 r 4

(ii) ( 3x²y²z² ) x ( 17xyz )

= 51x³y³z³

(iii) ( 15xy² ) x ( 17yz² )

= 255xy³z²

(iv) ( –5a²bc ) x ( 11ab ) x ( 13abc² )

= -715a⁴b³c³

(v) ( pq – 2r ) x ( pq – 2r )

= pq ( pq – 2r) – 2r( pq – 2r )

= p²q² – 2pqr – 2rpq + 4r²

= p²q² – 4pqr + 4r²

(vi) ( 3 p² + 2 q² ) x ( 2p² – 3q² )

2 3

= 3p² x 2p² – 3 p² x 3q² + 2q² x 2p² – 2q² x 3q²

2 2 3 3

= 6P 4 – 9p²q² + 4q²p² – 6q 4

2 2 3 3

= 3P 4 – 9p²q² + 4q²p² – 2q 4

2 3

Question 6. Which term is the like term similar to 24a²bc?

(a) 13 × 8a × 2b × c × a

(b) 8 × 3 × a × b × c

(d) 3 × 8 × a × b × b × c

Answer 6. Option (a)

Explanation: To find out the similar term as 24a²bc, let us find the product of each of the equations,

13 × 8a × 2b × c × a = 208a²bc
8 × 3 × a × b × c = 24abc
3 × 8 × a × b × c × c = 24abc²
3 × 8 × a × b × b × c = 24ab²c

Hence, we can get that option (a) is correct.

Question 7. Which of the following is an identity?

(a) (p + q)² = p² + q²

(b) p² – q² = (p – q)²

(d) (p + q)² = p² + 2pq + q²

Answer 7. Option (d)

Explanation: The equation (p + q)² = p² + 2pq + q² follows the first standard algebraic identity

( a + b )² = a² + 2ab + b². The rest of the other options do not follow any of the standard identities. Hence option (d) is correct.

Question 8. Fill in the blanks.

(a) (x + a) (x + b) = x² + (a + b)x + ________.

(b) The product of two terms with like signs is a ________ term.

(d) (a – b) _________ = a² – 2ab + b²

(e) a² – b² = (a + b ) __________.

(f) (a – b)² + ____________ = a² – b²

(g) (a + b)² – 2ab = ___________ + ____________

(h) The product of two polynomials is a ________

(i) The coefficient in – 37abc is __________.

(j) Number of terms in the expression a2 + bc × d is ________

As per the standard identity 4, (x + a) (x + b) = x² + (a + b)x + ab

(b) Positive

(d) ^2 or ( a – b)²

As per standard identity 2, (a – b)² = a² – 2ab + b²

(e) (a – b)

As per standard identity 3, (a + b ) ( a – b ) = a² – b²

(f) 2ab – 2b²

Let us solve the equation with x in the blank space. As per identity 2, (a – b)² = a² – 2ab + b².

Hence, a² – 2ab + b² + x = a² – b²

x = a² – b² – a² + 2ab – b²

x = 2ab – 2b²

(g) a² + b²

Using Identity 1 ( a + b )² = a² + 2ab + b²,

(a + b)² – 2ab = a² + 2ab + b² – 2ab = a² + b²

(h) Polynomial

Question 9. Solve the below using correct identities.

(b) 181² – 19²

(d) 2.07 × 1.93

= (50 – 2)²

As (a – b)² = a² – 2ab + b² , hence

(50 – 2)² = (50)² – 2 × 50 × 2 + (2)²

= 2500 – 200 + 4

= 2300 + 4

= 2304

(b) As a² – b² = (a – b) (a + b)

181² – 19² = (181 – 19) (181 + 19)

= 162 × 200

= 32400

497 x 505 = ( 500 – 3 ) (500 + 5 )

= 500² + (–3 + 5) × 500 + (–3) (5)

= 250000 + 1000 – 15

= 250985

(d) As (a + b) (a – b) = a² – b²

2.07 × 1.93 = (2 + 0.07) (2 – 0.07)

= 2² – 0.07²

= 3.9951

Question 10. The length of a rectangular box is ( x + 9y) and the area is x² + 12xy + 27y². Find the breadth.

Answer 10. Area of a rectangle = length x breadth, hence breadth = area / length.

breadth = x² + 12xy + 27y²

( x + 9y )

= x² + 9xy + 3xy + 27y²

( x + 9y )

= x ( x + 9y ) + 3y (x + 9y)

( x + 9y )

breadth = x + 3y

Question 11. With the help of identity (x + a) (x + b) = x² + (a + b) x + ab, find the following products.

(a) (x + 3) (x + 7)

(b) (4x + 5) (4x + 1)

(d) (4x + 5) (4x – 1)

(e) (2x + 5y) (2x + 3y)

(f) (2a²+ 9) (2a²+ 5)

(g) (xyz – 4) (xyz – 2)

Answer 11.

( x + 3 ) ( x + 7 )

= x² + ( 3 + 7 ) x + ( 3 x 7 )

= x² + 10x + 21

( 4x + 5 ) ( 4x + 1 )

= 16x² + ( 5 + 1 ) 4x + ( 5 x 1 )

= 16x² + 24x + 5

= 16x² + ( – 5 – 1 ) 4x + ( -5 x -1 )

= 16x² – 24x + 5

(d) (4x + 5) (4x – 1)

= 16x² + ( 5 + ( – 1 ) )4x + ( 5 x ( – 1 ) )

= 16x² + 16x – 5

(e) (2x + 5y) (2x + 3y)

= 4x² + ( 5y + 3y )2x + ( 5y x 3y )

= 4x² + 16xy + 15y²

(f) (2a²+ 9) (2a²+ 5)

= 4a 4 + ( 9 + 5 )2a² + ( 9 x 5 )

= 4a 4 + 28a² + 45

(g) (xyz – 4) (xyz – 2)

= x²y²z² + ( -4 – 2)xyz + ( – 4 x – 2)

= x²y²z² – 6xyz + 8

Question 12. The exponents of the variables in a polynomial are always

(a) Integers

(b) Positive integers

(d) Non-positive integers

Answer 12. (c) Non-negative integers

Explanation: A polynomial will have a non-zero coefficient and variables having non-negative integers as exponents. For example : a + b + r + q, 3ab, 5xyz – 10, 2a + 3b + 7z, etc.

Question 13. The product of a binomial and monomial is a

(a) Monomial

(b) Binomial

(d) None of these

Answer 13. (b) Binomial

Explanation: This can be demonstrated through an example below,

x ( y + z ) = xy + xz

This expression contains two terms, x is a monomial and ( y + z ) is a binomial.

The product of multiplying these terms results in a binomial product xy + xz.

Question 14. Using identities, find products for the below.

(f) 297 × 303

(g) 78 × 82

(i) 10.5 × 9.5

Answer 14.

71² = ( 70 + 1 )² Identity applied ( a + b )² = a² + 2ab + b²

= 70² + 2 ( 70 x 1 ) + 1²

= 4900 + 140 + 1

99² = ( 100 – 1 )² Identity applied ( a – b )² = a² – 2ab + b²

= 100² – 2 ( 100 x 1 ) + 1²

= 10000 – 200 + 1

= 9801

= 100² + 2 ( 100 x 2 ) + 2²

= 10000 + 400 + 4

= 10404

(d) 998² = ( 1000 – 2 )² Identity applied ( a – b )² = a² – 2ab + b²

= 1000² – 2 ( 1000 x 2 ) + 2²

= 1000000 – 4000 + 4

= 996004

(e) 5.2² = ( 5 + 0.2 )² Identity applied ( a + b )² = a² + 2ab + b²

= 5² + 2 ( 5 x 0.2 ) + 0.2²

= 25 + 2 + 0.04

= 27.04

(f) 297 × 303 = ( 300 – 3 ) ( 300 + 3 ) Identity applied ( a + b ) ( a – b ) = a² – b²

= 300² – 3²

= 90000 – 9

= 89991

(g) 78 × 82 = ( 80 – 2 ) ( 80 + 2 ) Identity applied ( a + b ) ( a – b ) = a² – b²

= 80² – 2²

= 6400 – 4

= 6396

(h) 8.9² = ( 9.0 – 0.1 )² Identity applied ( a – b )² = a² – 2ab + b²

= 9.0² – 2 ( 9.0 x 0.1 ) + 0.1²

= 81 – 1.8 + 0.01

= 79.21

(i) 10.5 x 9.5 = ( 10 + 0.5 ) ( 10 – 0.5 ) Identity applied ( a + b ) ( a – b ) = a² – b²

= 10² – 0.5²

= 100 – 0.25

= 99.75

Question 15. The Coefficient of y in the term −y is

Answer 15. (c) – 1

Explanation: Coefficient is defined as the numerical factor of a term.

Hence, the numerical factor/ coefficient of the term −y is −1

3 3

Question 16.Obtain the volume of rectangular boxes with the following length, breadth and height

respectively.

(a) 5a, 3a², 7a 4

(b) 2p, 4q, 8r

(d) a, 2b, 3c

Answer 16. The volume of a rectangular box is the product of its length,

breadth and height, i.e Volume = length x breadth x height.

Volumes are calculated as below,

(a) length = 5a, breadth = 3a², height = 7a 4

Volume = 5a x 3a² x 7a 4

(b) length = 2p, breadth = 4q, height = 8r

Volume = 2p x 4q x 8r

Volume = xy x 2x²y x 2xy²

(d) length = a, breadth = 2b, height = 3c

Volume = a x 2b x 3c

Question 17. State whether the following are True (T) or False (F):

(a) (a + b)² = a² + b²

(b) (a – b)² = a² – b²

(d) The product of two negative terms is a negative term.

(e) The product of one negative and one positive term is a negative term.

(f) The coefficient of the term – 6x²y² is – 6.

(g) p²q + q²r + r²q is a binomial

(h) An equation is true for all values of its variables.

Answer 17.

(a) False. ( a + b )² = a² + 2ab + b²

(b) False. ( a – b )² = a² – 2ab + b²

(d) False. The product of two negative terms is positive.

(g) False. The equation p²q + q²r + r²q consists of three terms; hence it is a trinomial.

(h) False. An equation is not true for all values of its variables. For example : 4x + 2 = 10 is true, only for x = 2.

Question 18. Show that LHS = RHS for the below equations.

(a) ( 3x + 7 )² – 84x = ( 3x – 7 )²

(b) ( 9p – 5q )² + 180pq = ( 9p + 5q )²

(d) (a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a) = 0

Answer 18.

(a) LHS = ( 3x + 7 )² – 84x

= (3x)² + 2 ( 3x x 7 ) + 7² – 84x

= 9x² + 42x + 49 – 84x

= 9x² – 42x + 49

RHS = ( 3x – 7 )²

= (3x)² – 2 ( 3x x 7 ) + 7²

Hence LHS = RHS

(b) LHS = ( 9p – 5q )² + 180pq

= (9p)² – 2 ( 9p x 5q ) + (5q)² + 180pq

= 81p² + 90pq + 25q²

RHS = ( 9p + 5q )²

= (9p)² + 2 ( 9p x 5q ) + (5q)²

= 81p² + 90pq + 25q²

= (4pq)² + 2 ( 4pq x 3q ) + (3q)² – ( (4pq)² – 2 ( 4pq x 3q ) + (3q)²)

= 16p²q² + 24pq² + 9q² – 16p²q² + 24pq² – 9q²

= 48pq²

RHS = 48pq²

Hence LHS = RHS

(d) LHS = (a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a)

= a² + ab – ba – b² + b² + bc – cb – c² + c² + ca – ac – a²

= 0

RHS = 0

Question 19. Expand the following, using suitable identities.

(a) ( xy + yz )²

(b) ( x²y – xy² )²

(d) ( 0.9p – 0.5q )²

(e) ( x² + y² ) ( x² – y² )

Answer 19.

(a) (xy + yz)²

= (xy)² + 2 (xy x yz ) + (yz)²

= x²y² + 2xy²z + y²z²

(b) (x²y – xy²)²

= (x²y)² – 2 (x²y x xy²) + (xy²)²

= x 4 y² – 2x³y³ + x²y 4

= (7x)² + 2 (7x x 5) + (5)²

= 49x² + 70x + 25

(d) (0.9p – 0.5q)²

= (0.9p)² – 2 ( 0.9p x 0.5q) + (0.5q)²

= 0.81p² – 0.9pq + 0.25q²

= x 4 – x²y² + y²x² – y 4

= x 4 – y 4

Question 20. Select the correct option of volume of a rectangular box with length = 2ab, breadth = 3ac and height = 2ac

(a) 12a³bc²

(d) 2ab +3ac + 2ac

Answer 20. Option (a)

Explanation: The formula for calculating the volume of a rectangular box is

Volume = length x breadth x height

With the length of the input = 2ab, breadth = 3ac and height = 2ac

Volume = 2ab x 3ac x 2ac

= 12a³bc²

Benefits of Solving Important Questions Class 8 Mathematics Chapter 9

Practising the questions from Important Questions Class 8 Mathematics Chapter 9 available on the Extramarks website will benefit the students in grasping the chapter concepts like variables, terms, and standard identities easily and solving the equations with better understanding and avoiding mistakes. Solving the important questions of the chapter rigorously will help you score well in the examination.

A few of the benefits of referring to Important Questions Class 8 Mathematics Chapter 9 are:

The study and practice materials are based on the latest versions of the CBSE syllabus and NCERT guidelines. Students can rely upon these materials to get well versed in the examination’s basic question/answer format.
Important Questions Class 8 Mathematics Chapter 9 contains various questions, including MCQs, long answer questions, etc., collated carefully by referring to some of the most trusted sources like NCERT textbooks, NCERT exemplar, past years’ question papers and other sources.
By thoroughly practising these tricky questions from the Important Questions Class 8 Mathematics Chapter 9, students can analyse their weak areas of Chapter 9 Algebra and overcome them before facing their final examinations.
All the Important Questions Class 8 Science Chapter 9 has step-by-step solutions to all the questions in the textbook. It will benefit you to read through the problem carefully and figure out what it’s about.

To access the answers given in Important Questions Class 8 Mathematics Chapter 9, you can register on the Extramarks website. Furthermore, students can access the other study materials from Classes 1 to 12 by clicking on the below links:

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Q.1 Using identity, find the value of (4.7) 2 .

Marks: 2 Ans

Use the identity as (a b) 2 = a 2 2ab + b 2 .

4.7 2 = 5 0.3 2 = 5 2 2 — 5 — 0.3 + 0.3 2 = 25 3.0 + 0.09 = 22.09

Hence, the required value is 22.09.

Q.2 Simplify: (a + 2) (c 4) + (a 2) (c + 2) + 2 (ac + 17)

(a + 2) (c 4) + (a 2) (c + 2) + 2 (ac + 17) = ac 4a + 2c 8 + ac + 2a 2c 4 + 2ac + 34 = 4ac 2a + 22

Q.3 The value of 1001 × 1004 is

Marks: 1 Ans [ 2049078 ]

Q.4 If the length of a rectangle is 2x 2 + 3 units and its breadth is 2x 2 7 units. What is the area and perimeter of the rectangle

Marks: 4 Ans

(x + a) (x + b) = x 2 + x (a + b) + ab Area = length × breadth = (2x 2 + 3) × (2x 2 7) = (2x 2 ) 2 + 2x 2 (3 7) + 3(7) = 4x 4 8x 2 21 square units Perimeter = 2(length + breadth) = 2(2x 2 + 3 + 2x 2 7) = 2(4x 2 4) = 8x 2 8 units

If x 2 + 1 x 2 = 4 , what is the value of x + 1 x

Given: x 2 + 1 x 2 = 4 using identities: (a + b) 2 = a 2 + b 2 + 2ab x + 1 x 2 = x 2 + 1 x 2 + 2 x × 1 x = 4 + 2 = 6

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Cbse class 8 maths important questions, chapter 1 - rational numbers.

Chapter 2 - Linear Equations in One Variable

Chapter 3 - understanding quadrilaterals, chapter 4 - practical geometry, chapter 5 - data handling, chapter 6 - squares and square roots, chapter 7 - cubes and cube roots, chapter 8 - comparing quantities, chapter 10 - visualising solid shapes, chapter 11 - mensuration, chapter 12 - exponents and powers, chapter 13 - direct and inverse proportions, chapter 14 - factorisation, chapter 15 - introduction to graphs, chapter 16 - playing with numbers, faqs (frequently asked questions), 1. how can i score good marks in class 8 mathematics.

One of the most effective ways to understand and remember the concepts is by practising a variety of questions at the end of the chapter. The Extramarks team understands the importance of practising the questions while preparing for the examinations and provides a full list of Important Questions Class 8 Mathematics Chapter 9. Students can practise these advanced levels of questions on the Extramarks website to become familiar with different types of questions and perform well in their exams.

2. What do the Important Questions Class 8 Mathematics Chapter 9 include?

The Important Questions Class 8 Mathematics Chapter 9 includes a variety of easy as well as difficult questions from different sources like the NCERT textbook, NCERT solutions, NCERT Exemplars, and other standard books for students to practise and excel in their school and competitive examinations. The questions come along with detailed step-by-step solutions, which are created by Extramarks Mathematics experts who completely feel the pulse of the students while preparing such a questionnaire. Each and every topic has been taken care of to avoid unnecessary stress and anxiety students might face while learning. It gives the students enough practice to boost their confidence level. The more you practise, the better you will get. That’s the key to success.

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NCERT Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities

The NCERT solutions for Class 8 maths Chapter 9 Algebraic Expressions and Identities provides an introduction to a useful mathematical tool to handle the ever changing world we live in. If there is one thing that is constant about the universe, it is ‘change’ so it was felt early on by the mathematicians to have a framework such that it can handle the change and everytime the calculation need not be done from scratch. For example, when they studied geometry and measured the area of one circle thereafter using mathematics they devised a formula into which everytime you feed into the value of the radius of the circle it would give the area of the corresponding circle.

This power to have an expression is such that based on the value of the input it will give different answers, thus greatly enhancing the usage of mathematics . Let us take an example in the NCERT solutions Class 8 maths Chapter 9. Consider that in a school , for students of class 7, one notebook per student is needed and for students of class 8 two notebooks per student is needed. If we consider the number of students in class 7 as ‘x’ and number of students in class 8 as ‘y’ then the number of books needed in total would be ‘x + 2y’. The Class 8 maths NCERT solutions Chapter 9 Algebraic Expressions and Identities will help students understand both the utility and the application of such expressions and also you can find some of these in the exercises given below.

NCERT Solutions Class 8 Maths Chapter 9 Ex 9.1
NCERT Solutions Class 8 Maths Chapter 9 Ex 9.2
NCERT Solutions Class 8 Maths Chapter 9 Ex 9.3
NCERT Solutions Class 8 Maths Chapter 9 Ex 9.4
NCERT Solutions Class 8 Maths Chapter 9 Ex 9.5

NCERT Solutions for Class 8 Maths Chapter 9 PDF

Algebraic Expressions and Identities is an important and interesting concept to understand the nature of mathematics, and the NCERT solutions Class 8 maths Chapter 9 Algebraic Expressions and Identities has made sure to analyze this topic step by step, covering the easy examples and exercise questions first, then gradually moving on to the complicated ones so that the students feel motivated throughout their learning. The exercise questions in each segment of the chapter can be accessed through the links below :

☛ Download Class 8 Maths NCERT Solutions Chapter 9

NCERT Class 8 Maths Chapter 9 Download PDF

$NCERT Solutions Class 8 Math Chapter 9 Algebraic Expressions And Identities 1$

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities

Algebraic expressions play an important role in giving the problems an easy frame that can be understood properly and then solved accordingly. Hence, the study of algebra holds an important place in mathematics. A brief classification of questions in each exercise of NCERT Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities can be seen as below:

Class 8 Maths Chapter 9 Ex 9.1 - 4 Questions
Class 8 Maths Chapter 9 Ex 9.2 - 5 Questions
Class 8 Maths Chapter 9 Ex 9.3 - 5 Questions
Class 8 Maths Chapter 9 Ex 9.4 - 3 Questions
Class 8 Maths Chapter 9 Ex 9.5 - 8 Questions

☛ Download Class 8 Maths Chapter 9 NCERT Book

Topics Covered: The Class 8 math NCERT solutions Chapter 9 covers the concept of coefficients and variables, factors , terms, polynomials , the addition of polynomials , multiplication of polynomials , and algebraic identities .

Total Questions: Class 8 maths Chapter 9 Algebraic Expressions and Identities consists of 25 questions out of which 17 are easy and quick to solve, while the remaining 8 may require a longer time.

List of Formulas in NCERT Solutions Class 8 Maths Chapter 9

The NCERT solutions Class 8 maths Chapter 9 outlines what an expression is, how it is made and what are the different parts in an expression. Further, how to perform operations on the expressions like those of addition , multiplication , etc., and the explanation of some standard identities is drafted in this chapter. Some of the important facts and formulas covered in NCERT solutions for Class 8 maths Chapter 9 are given below :

Expressions are made up of terms which in turn are made of coefficients and variables.
Operations involving expressions follow the distributive law.
Below are the three identities which hold true for any value of variable
(a + b) 2 = a 2 + 2ab + b 2
(a – b) 2 = a 2 – 2ab + b 2
(a + b) (a – b) = a 2 – b 2

Important Questions for Class 8 Maths NCERT Solutions Chapter 9

CBSE Important Questions for Class 8 Maths Chapter 9 Exercise 9.1

CBSE Important Questions for Class 8 Maths Chapter 9 Exercise 9.2

CBSE Important Questions for Class 8 Maths Chapter 9 Exercise 9.3

CBSE Important Questions for Class 8 Maths Chapter 9 Exercise 9.4

CBSE Important Questions for Class 8 Maths Chapter 9 Exercise 9.5

NCERT Solutions for Class 8 Maths Video Chapter 9

NCERT Class 8 Maths Videos for Chapter 9
Video Solutions for Class 8 Maths Exercise 9.1


Video Solutions for Class 8 Maths Exercise 9.2



Video Solutions for Class 8 Maths Exercise 9.3



Video Solutions for Class 8 Maths Exercise 9.4


Video Solutions for Class 8 Maths Exercise 9.5

FAQs on NCERT Solutions Class 8 Maths Chapter 9

Why are ncert solutions class 8 maths chapter 9 important.

The NCERT Solutions Class 8 Maths Chapter 9 has well-drafted examples to explain the concept of algebraic expressions and identities. The components that make an expression have been dealt with in detail to bring better clarity to the subject and instilling the necessary confidence in the students. The CBSE board asks the students to refer to the NCERT books which is proof of their exceptional quality.

Do I Need to Practice all the Questions Provided in NCERT Solutions Class 8 Maths Algebraic Expressions and Identities?

Expressions are like mathematical entities of their own and they have widespread applications. This chapter provides the opportunity to learn about this very important and useful concept. Additionally, expressions can vary from simple to complex, and while the concept is simple, its applications can be amazingly creative. Owing to these reasons, one must make sure to study the application of algebraic expressions. With plenty of examples and exercise questions in NCERT Solutions Class 8 Maths Algebraic Expressions and Identities, the students can explore every basic detail.

What are the Important Topics Covered in NCERT Solutions Class 8 Maths Chapter 9?

The NCERT Solutions Class 8 Maths Chapter 9 covers the concept of Algebraic Expressions and Identities in detail with the help of proper explanations and most importantly by introducing the components which make up an expression that is the ‘terms’. It further zeroes on what makes up a term” that is the ‘coefficient' and ‘variable’, then takes a macroscopic view of how expressions can be of different types and how they operate.

How Many Questions are there in NCERT Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities?

The NCERT Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities has 25 questions, 17 of which are short-form, while 8 are long-form questions. The students will be required to calculate or identify Algebraic Expressions and Identities of numbers.

How CBSE Students can utilize NCERT Solutions Class 8 Maths Chapter 9 effectively?

The students should pay attention to the highlight sections in the NCERT Solutions Class 8 Maths Chapter 9 as they speak about important facts. These should be noted down and revised along with a consistent practice of solved examples and exercise questions. In this way, the students can utilize the NCERT Solutions Class 8 Maths Chapter 9 effectively.

Why Should I Practice NCERT Solutions Class 8 Maths Algebraic Expressions and Identities Chapter 9?

The NCERT Solutions Class 8 Maths Algebraic Expressions and Identities Chapter 9 has well-explained examples and a logical step-by-step explanation of the facts with proper problem-solving statements. This will greatly help the students in learning how to solve exam questions and display their responses with correct logic. As a result, kids must make the most of the chapter's content by practicing the examples and solving all the questions.

CBSE- Algebraic Expressions and Identities
Sample Questions

Algebraic Expressions and Identities-Sample Questions

STUDY MATERIAL FOR CBSE CLASS 8 MATH
Chapter 1 - Algebraic Expressions and Identities
Chapter 2 - Comparing Quantities
Chapter 3 - Cubes and Cube Roots
Chapter 4 - Data handling
Chapter 5 - Direct and Inverse Proportions
Chapter 6 - Exponents and Powers
Chapter 7 - Factorization
Chapter 8 - Introduction to Graphs
Chapter 9 - Mensuration
Chapter 10 - Playing with Numbers
Chapter 11 - Practical Geometry
Chapter 12 - Squares and Square Roots
Chapter 13 - Visualizing Solid Shapes
Chapter 14 - Linear Equations in One Variable
Chapter 15 - Rational Numbers
Chapter 16 - Understanding Quadrilaterals

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Algebraic Expressions and Identities Class 8 Notes CBSE Maths Chapter 9 (Free PDF Download)

Revision Notes
Chapter 9 Algebraic Expressions And Identities

Revision Notes for CBSE Class 8 Maths Chapter 9 Algebraic Expressions and Identities - Free PDF Download

For a Class 8 student, it becomes quite difficult for the student to understand the rise in the level of complexity from previous classes. Also, for subjects like Mathematics, it is important for you to be attentive at all times. The subject influences a lot of importance in both your educational and personal life. For a better level of understanding, it is highly important to conquer your basic concepts and formulas of the chapter first and then further move to solve the numerical questions given in the chapter.

Vedantu is a platform that provides free NCERT Solution and other study materials for students. Science Students who are looking for NCERT Solutions for Class 8 Science will also find the Solutions curated by our Master Teachers really Helpful.

You can also download NCERT Solutions Class 8 Maths to help you to revise complete syllabus ans score more marks in your examinations.

Download CBSE Class 8 Maths Revision Notes 2024-25 PDF

Also, check CBSE Class 8 Maths revision notes for All chapters:






Chapter 9: Algebraic Expressions and Identities Notes

Access Class 8 Maths Chapter 9 - Algebraic Expressions and Identities

What are expressions.

Expressions are mathematical sentences which include at least two constant, variables or both connected by mathematical operations.

For example: \[3+5,x-y,5+y\] etc.

Number line and expression: An expression can be shown on a number line as shown by the example below

For example: To show $x+3$ on a number line

Make $x$ at any distance on the number line then move $3$ units right of $x$. The point P shows $x+3$ on a number line

Similarly, if we have to show $x-4$ on the number line Make $x$ at any distance on the number line then move $4$ units left of $x$.

Terms, Factors and Coefficients

Terms are the building blocks of an expression. It may be single number, single variable, product of variables, product of numbers or product of number and variable both.

For example: In expression $3x+5y$ there are two terms $3x$ and $5y$

Factors are number or algebraic expressions that completely divide another number or expression.

For example: In expression $5y$ the factors are $5$ and $y$

The numerical factor of a term is called coefficients

For example: In expression $5x+7y$ , $5$ and $7$ are the coefficients of $x$ and $y$ respectively

Monomials, Binomials, Polynomials

Expression that contains only one term is called monomial

For example: $5y,3x,{{x}^{2}},9,ab$ etc. are monomials

Expression that contains two term is called binomial

For example: $2x+y,4{{y}^{2}}+z,ab+mn$ etc. are binomials

Expression that contains three term is called trinomial

For example: $x+y+z,2a+b+7c,{{a}^{2}}+6b+{{c}^{2}}$ etc.

An expression containing one or more terms with non-zero coefficient and with variables having non negative exponents is called a polynomial.

A polynomial may contain any number of terms.

For example: $2x+y,4xy,a+b+c,{{m}^{2}}$ etc. are polynomials

Like and Unlike Terms

Like terms are those terms which have the same variable, power of the variable should also be same and coefficient can be different.

For example: $6x$ and $8x$ are the like terms

Unlike terms are opposite of like terms it has different variables.

For example: $5y$ and $9a$ are unlike terms

Addition and Subtraction of Algebraic Expressions

In addition, like terms are added.

For example: Add of $3a+5b+2ab$ and $2a+3b+7ab$

Write like terms below one another then add

$3a+5b+2ab $

$+2a+3b+7ab $

$ \overline{5a+8b+9ab} $

In subtraction also only like terms are subtracted.

For example: Subtract ${{x}^{2}}+2x-4xy$ and $3{{x}^{2}}+2xy$

Write like terms below one another then subtract

$ {{x}^{2}}+2x-4xy $

$ +3{{x}^{2}}+2xy $

$ \overline{-2{{x}^{2}}+2x-6xy} $

Multiplication of Algebraic Expression

1. Multiplying a Monomial by a Monomial

The product of two monomial is always a monomial

For example: Multiplication of $20xy$ and $4z$ is $20xy\times 4z=80xyz$

Multiplication of $7z,2{{x}^{2}}$ and $4y$ is $7z\times 2{{x}^{2}}\times 4y=56{{x}^{2}}yz$

2. Multiplying a Monomial by a Polynomial

Use distributive law to multiply a monomial by a polynomial i.e., multiply monomial to each term of polynomial

For example: Multiplication of $6x$ and $3{{x}^{2}}+5y$ is

$\left( 6x \right)\times \left( 3{{x}^{2}}+5y \right)=\left( 6x\times 3{{x}^{2}} \right)+\left( 6x\times 5y \right)$

$=18{{x}^{3}}+30xy$

3. Multiplying a Polynomial by a Polynomial

Multiply each term of a polynomial by each term of another polynomial then combine like terms if any

For example: Multiplication of $\left( 2x+3y \right)$ and $\left( 2x-3y+z \right)$ is

$\left( 2x+3y \right)\times \left( 2x-3y+z \right)=\left( 2x \right)\left( 2x-3y+z \right)+\left( 3y \right)\left( 2x-3y+z \right)$

$=\left( \left( 2x \right)\left( 2x \right)-\left( 2x \right)\left( 3y \right)+\left( 2x \right)\left( z \right) \right)+\left( \left( 3y \right)\left( 2x \right)-\left( 3y \right)\left( 3y \right)+\left( 3y \right)\left( z \right) \right)$

$=\left( 4{{x}^{2}}-6xy+2xz \right)+\left( 6xy-9{{y}^{2}}+3yz \right)$

$=4{{x}^{2}}+2xz-9{{y}^{2}}+3yz$

An equation is not true for any value of variable but for certain values.

The equation which is always true for any value of variables is called identity.

Standard Identities

The following identities are known as standard identities

${{\left( a+b \right)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab$

${{\left( a-b \right)}^{2}}={{a}^{2}}+{{b}^{2}}-2ab$

$\left( a+b \right)\left( a-b \right)={{a}^{2}}-{{b}^{2}}$

Another Useful Identity

$\left( x+a \right)\left( x+b \right)={{x}^{2}}+\left( a+b \right)x+ab$

These identities make calculation easier.

Download Revision Notes Class 8 Maths Chapter 9 - Free PDF

Class 8 students preparing for Chapter 9 Algebraic Expressions and Identities may wonder where to find the exact Algebraic Expressions and Identities Class 8 Notes for a better understanding of the chapter. This is the reason why Vedantu is bringing Algebraic Expressions and Identities Class 8 Note right in front of you. These revision notes include all the important topics and formulas of the chapter in one single page so that you don't face any problem.

Revision Notes Class 8 Maths Chapter 9 proves to be tremendously important for the students eager to complete the entire chapter in less time. These revision notes are prepared by subject matter experts at Vedantu who have extensive years of experience in teaching Mathematics. Algebraic Expressions and Identities Class 8 Notes will improve your knowledge and will be useful in understanding the important concepts of the chapter before the examination.

Download Revision Notes Class 8 Maths for better preparation of Chapter. These revision notes are designed as per the latest NCERT syllabus issued by the CBSE board. Students of class 8 can download free Class 8 Maths Chapter 9 Revision Notes just with a single click on the PDF link given on this page.

A Few Glimpses of Chapter 9 Algebraic Expressions and Identities

With the previous basic knowledge of algebraic expression or simple expressions such as 9y, 5p - 4q, 3p² -q, etc, Class 8 Chapter 9 Algebraic Expressions and Identities will help you to explore the world of Algebraic Expression.

Algebraic Expressions

An algebraic expression is an expression that is formed using variables and constants. The expression 9y - 5 is formed using variable y and constant 9 and 5. We know that the value of y in expression 9y - 5 can be anything. It can be either 9, 5, 0, 9/5. etc. There can be unlimited different values. It is important to note that the value of expression varies with the value chosen for the variables it includes. Hence, the value of 9y - 5 goes on changing as y takes different values. For example, when y = 2, 9(2) - 5 = 18 - 5 = 13, when y = 0 , 9(0) - 5 = - 5 etc.

Algebraic Identities

In Mathematics, algebraic identity is an equality that holds despite the value chosen for its variables. Generally, Algebraic identities are used to simplify or rearrange algebraic expression. Through definition, we can state that two sides of identities are replaceable., so we can easily replace one with the other at any time. For example, the identity ( p + q)² = p² + q² + 2pq is true for all the choices of p and q, whether they are complex or real numbers.

Chapter 9 Algebraic Expressions and Identities includes seven exercises and 9 different topics and the Class 8 Maths Revision Notes Chapter 9 PDF provided by Vedantu includes the short and brief explanation of every topic given in the chapter. Now, let us look at the topics discussed in this chapter.

What are Expressions

Terms, Factors, Coefficients

Multiplication of Algebraic Expressions

Multiplication of two Monomials

Multiplication of three or more Monomials

Multiplication of Monomials by Binomials

Multiplication of Monomials by Trinomials

Multiplication of Polynomial by Polynomial

Multiplication of Binomial by Binomial

Multiplication of Binomial by Trinomial

What is Identity?

Applying Identities

Download Class 8 Maths Revision Notes Chapter 9 now and gets the brief explanations of all the topics discussed above.

Key Benefits of Class 8 Maths Revision Notes Chapter 9

Some of the key benefits of Class 8 Maths revision notes Chapter 9 are discussed below:

Class 8 Maths Revision Notes Chapter 9 is written in a simple language. Explanations of the topics are to the point. This will help students to go through the important concepts of the chapter with much ease and save time.

With Vedantu’s Class 8 revision notes Maths Ch 9, you don't need to wait for someone else to make you understand the concepts or important topics of the chapter. If you refer to these notes, you will be able to understand all the topics by yourself. Simple language and simple explanation of the topics will make your learning process easy.

The explanations of the concepts are not written in boring and big paragraphs. All the different topics of the chapter are explained with the help of examples. The example help will surely help in better understanding of the chapter. You can easily remember the concepts with the help of examples that are provided by Vedantu.

Class 8 revision notes Maths Ch 9 provides all the concepts and the topics of the chapter right in front of you. It will not let you miss any topic that is of the greatest importance for your examination. Once you revise these notes, you can be sure of one thing that you will be easily able to solve Algebraic Expressions and Identities numerical questions asked in the examination.

You can download Class 8 Maths revision notes Chapter 9 Pdf for free. You can download these revision notes on your PC, laptops as well your mobile phone as per your needs.

Conclusion

The Algebraic Expressions and Identities Class 8 Notes by Vedantu help students understand mathematical concepts in an easy way. This resource, available for free download, covers Chapter 9 of CBSE Maths. The importance of this topic lies in mastering algebraic expressions and identities, which are fundamental in mathematics. These notes break down complex ideas, making them accessible for Class 8 students. With a focus on key concepts, this material aids in building a strong foundation for solving mathematical problems. The free PDF download is a valuable tool for students to enhance their understanding of algebraic expressions and identities.

FAQs on Algebraic Expressions and Identities Class 8 Notes CBSE Maths Chapter 9 (Free PDF Download)

1. What are algebraic expressions and identities?

Algebraic expressions: expressions that are formed using integer constants, variables, and algebraic operations.

Example: 9x 3 – 3x 2 +6xy – z

Algebraic Identities: it is referred to as equality or an expression that always holds true for every value of variables in them.

Example: (a + b) 3 = a 3 + b 3 + 3ab (a + b)

You can find detailed explanations of these terms on Vedantu's Notes for Class 8 Mathematics Chapter 9 "Algebraic Expressions and Identities."

2. How should I use Vedantu’s notes to study Chapter 9 of Class 8 Mathematics?

Class 8 Mathematics Chapter 9 "Algebraic Expressions and Identities'' introduces the students to several new terms and concepts. Students must understand these concepts and memorize the terms to help them in mastering this chapter. You can use Vedantu's Revision Notes for "Algebraic Expressions and Identities'' to go over all the important concepts of the chapter in one place. You can also use these notes for a quick revision before every study session and also before exams.

3. Are Vedantu’s revision notes for Chapter 9 of Class 8 Mathematics reliable?

Yes, the notes provided by Vedantu are 100% reliable. The notes are carefully prepared by expert Mathematics teachers. These experienced teachers prepare the revision notes intending to provide the students with short but comprehensive notes to help them in their studies. Particular attention is given to the fact that every important piece of information from the chapter is mentioned in our revision notes. Our teachers also add simplified explanations of their own to aid in students' understanding of the concepts.

4. Is Chapter 9 of Class 8 Mathematics difficult?

Chapter 9 of Class 8 Mathematics may appear difficult to some students initially. The reason for this is that there are many new terms and concepts that students may find complicated. However, the fact of the matter is that the chapter is extremely intriguing and once you get the hang of the concepts you will enjoy solving all 5 exercises. Make efforts to understand the chapter and then treat every question like an interesting puzzle and you find this chapter a piece of cake.

5. How can I memorize the new terms taught in Chapter 9 of Class 8 Mathematics?

Chapter 9 of Class 8 Mathematics contains many terms to understand and memorize. These include expression, identities, terms, variables, constants, like and unlike terms, monomials, binomials, trinomials, and polynomials. You will also be introduced to some standard algebraic identities that you must memorize as you will be using these identities in upcoming grades as well. Go over every term and identity and daily to memorize them. Write the identities in a separate notebook and go over them. Refer to Vedantu's revision notes for daily revision.

NCERT Solutions

Study materials for class 8.

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NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities

October 4, 2019 by Sastry CBSE

Class 8 Maths Algebraic Expressions and Identities Exercise 9.1
Class 8 Maths Algebraic Expressions and Identities Exercise 9.2
Class 8 Maths Algebraic Expressions and Identities Exercise 9.3
Class 8 Maths Algebraic Expressions and Identities Exercise 9.4
Class 8 Maths Algebraic Expressions and Identities Exercise 9.5
Algebraic Expressions and Identities Class 8 Extra Questions

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.1

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.1 Q1

Ex 9.1 Class 8 Maths Question 3. Add the following: (i) ab – bc, bc – ca, ca – ab (ii) a – b + ab, b – c + bc, c – a + ac (iii) 2p 2 q 2 – 3pq + 4, 5 + 7pq – 3p 2 q 2 (iv) l 2 + m 2 , m 2 + n 2 , n 2 + l 2 , 2lm + 2mn + 2nl Solution: (i) Given: ab – bc, bc – ca, ca – ab We have (ab – bc) + (bc – ca) + (ca – ab) (Adding all the terms) = ab – bc + bc – ca + ca – ab = (ab – ab) + (bc – bc) + (ca – ca) (Collecting the like terms together) = 0 + 0 + 0 = 0

(ii) Given: a – b + ab, b – c + bc, c – a + ac We have (a – b + ab) + (b – c + bc) + (c – a + ac) (Adding all the terms) = a – b + ab + b – c + bc + c – a + ac = (a – a) + (b – b) + (c – c) + ab + bc + ac (Collecting all the like terms together) = 0 + 0 + 0 + ab + bc + ac = ab + bc + ac

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.1 Q3

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NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions And Identities are provided below. Our solutions covered each questions of the chapter and explains every concept with a clarified explanation. To score good marks in Class 8 Mathematics examination, it is advised to solve questions provided at the end of each chapter in the NCERT book.

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions And Identities are prepared based on Class 8 NCERT syllabus, taking the types of questions asked in the NCERT textbook into consideration. Further, all the CBSE Class 8 Solutions Maths Chapter 9 are in accordance with the latest CBSE guidelines and marking schemes.

Class 8 Maths Chapter 9 Exercise 9.1 Solutions

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.1 00001

Class 8 Maths Chapter 9 Exercise 9.2 Solutions

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.2 00001

Class 8 Maths Chapter 9 Exercise 9.3 Solutions

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.3 00001

Class 8 Maths Chapter 9 Exercise 9.4 Solutions

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.4 00001

Class 8 Maths Chapter 9 Exercise 9.5 Solutions

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.5 00001

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MCQ Questions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities with Answers

We have compiled the NCERT MCQ Questions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities with Answers Pdf free download covering the entire syllabus. Practice MCQ Questions for Class 8 Maths with Answers on a daily basis and score well in exams. Refer to the Algebraic Expressions and Identities Class 8 MCQs Questions with Answers here along with a detailed explanation.

Algebraic Expressions and Identities Class 8 MCQs Questions with Answers

Choose the correct option.

Question 1. Which of the following is the numeral coefficient of – 3x²y²? (a) 4 (b) 3 (c) 2 (d) -3

Answer: (d) -3

Question 2. What kind of polynomial is -5abc? (a) Monomial (b) Binomial (c) Trinonial (d) None of the above

Answer: (a) Monomial

Question 3. The value ofx² – 2yx + y² when x= 1; y = 2 is (a) 1 (b) 2 (c) 4 (d) 5

Answer: (a) 1

Question 4. How many terms are there in the expression 7 – 3x²y? (a) 1 (b) 2 (c) 3 (d) 4

Answer: (b) 2

Question 5. Which of the following is a binomial? (a) 3xy (b) 41 + 5m (c) 2x + 3y-5 (d) 4a – 7ab + 3b + 12

Answer: (b) 41 + 5m

Question 6. The sum of -7x, 3x and 11x (a) – 7x (b) 21x (c) 7x (d) -21x

Answer: (c) 7x

Question 7. What do you get when you subtract. -3xy from 5xy? (a) 3xy (b) 5xy (c) 8xy (d) 2xy

Answer: (c) 8xy

Question 8. The area of a rectangle with length 2l²m and breadth 31m² is (a) l³m³ (b) 2l³m³ (c) 4l³m³ (d) 6l³m³

Answer: (d) 6l³m³

Question 9. The volume of the cuboid of dimensions x, y, z is (a) x²y²z² (b) x³y³z³ (c) xyz (d) x²y²z

Answer: (b) x³y³z³

Question 10. The value of (x + y) (x + y) + (y – z) (y + z) + (z – x) (z + x) is equal to (a) 3x² (b) 3y² (c) 3z² (d) 0

Answer: (d) 0

Question 11. Which of the following is the numerical coefficient of x² y²? (a) 0 (b) 1 (c) x² (d) y²

Answer: (b) 1

Question 12. Which of the following is the numerical coefficient of -5xy? (a) 5 (b) x (c) 5 (d) y

Answer: (c) 5

Fill in the blanks

Question 1. The coefficient of-5x is ………………

Question 2. An expression having only one term is called ………………

Answer: monomial

Question 3. An expression having only three terms is called ………………

Answer: trinomial

Question 4. The product of (4x + y) (4x – y) is ………………….

Answer: 16x² – y²

Question 5. The sum of a a – b + 3 and 3a + 2b + 5 is ……………….

Answer: 4a + b + 8

Hope the information shed above regarding NCERT MCQ Questions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 8 Maths Algebraic Expressions and Identities MCQs Multiple Choice Questions with Answers, feel free to reach us so that we can revert back to us at the earliest possible.

Class 8 Maths MCQs
Chapter 9 Algebraic Expression and Identities

Class 8 Maths Chapter 9 Algebraic Expressions and Identities MCQs

Class 8 Maths Chapter 9 Algebraic Expressions and Identities MCQs (Questions and Answers) are provided online here for students. These multiple-choice questions have been designed by experts referring to the latest CBSE syllabus (2022-2023) and NCERT guidelines. The objective questions are provided chapter-wise at BYJU’S. Also, learn important questions for class 8 Maths here.

Practice more and test your skills on Class 8 Maths Chapter 9 Algebraic Expressions and Identities MCQs with the given PDF here.

MCQs Questions on Class 8 Algebraic Expressions and Identities

Multiple choice questions (MCQs) are available for Class 8 chapter 9 Algebraic Expressions and Identities chapter. For all the problems, there are four multiple options given among which one is the right answer. Solve each question and choose the correct answer.

1. An algebraic expression that contains only one term is called:

A. Monomial

B. Binomial

C. Trinomial

D. None of the above

Example: 2x is a monomial

2. 5x+6y is a:

Explanation: The expression containing two terms is called binomial.

3. The algebraic expression 3x+2y+6 is a:

Explanation: The algebraic expression containing three terms is called a trinomial. Here, 3x, 2y and 6 are three terms.

4. A polynomial contains _______ number of terms:

Explanation: A polynomial can contain any number of terms, i.e. one or more than one.

5. In which of the following, the two expressions are like terms?

A. 7x and 7y

B. 7x and 9x

C. 7x and 7x 2

D. 7x and 7xy

6. If we add, 7xy + 5yz – 3zx, 4yz + 9zx – 4y and –3xz + 5x – 2xy, then the answer is:

A. 5xy + 9yz +3zx + 5x – 4y

B. 5xy – 9yz +3zx – 5x – 4y

C. 5xy + 10yz +3zx + 15x – 4y

D. 5xy + 10yz +3zx + 5x – 6y

Explanation: Given, 7xy + 5yz – 3zx, 4yz + 9zx – 4y and –3xz + 5x – 2xy.

If we add the three expressions, then we need to combine the like terms together.

(7xy – 2xy) + (5yz + 4yz) – 3zx + 9zx – 3xz – 4y + 5x

= 5xy + 9yz + 3zx + 5x – 4y

7. If we subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3, then the answer is:

A. 8a+2ab+2b+15

B. 8a+2ab+2b-15

C. 8a-2ab+2b-15

D. 8a-2ab-2b-15

Explanation: (12a – 9ab + 5b – 3) – (4a – 7ab + 3b + 12)

= 12a – 9ab + 5b – 3 – 4a + 7ab -3b-12

= (12 – 4)a – (9 – 7)ab + (5 – 3)b – 3 – 12

= 8a – 2ab + 2b – 15

8. If we multiply 5x and (– 4xyz), then we get:

A. 20x 2 yz

B. -20x 2 yz

Explanation: (5x) x (-4xyz)

= 5 × x × (-4) × x × y × z

= -20x 1+1 yz

= -20x 2 yz

9. The product of 4x and 0 is:

Explanation: Any value multiplied by zero is zero.

10. The volume of a cuboid with length, breadth and height as 5x, 3x 2 and 7x 4 respectively is:

Explanation: Volume of cuboid = Length × breadth × height

V = 5x × 3x 2 × 7x 4

V = 105 x 1+2+4

V = 105x 7 cubic units

11. The product of 5x and 3y is:

Answer: (D) 15xy

(5x)(3y) = 15xy

12. The product of 6x and -11x is:

Answer: B. -66x²

(6x) (-11x) = –66x²

13. The area of a rectangle whose length and breadth are 3y and 9y² respectively is:

Answer: C. 27y³

Explanation:

Area of rectangle = length x breadth = 3y x 9y² = 27y³.

14. The area of a rectangle that has length = 2a²b and breadth = 3ab² is:

Answer: A. 6a³b³

Area of rectangle = (2a²b)(3ab²) = 6a³b³

15. The side of a cube is 2a. Find the volume of the cube.

Answer: C. 8a³

Volume of the cube = 2a × 2a × 2a = 8a³

16. Multiplication of monomials x², (–x)³, (–x) 4 is equal to:

Answer: A. x 9

Explanation: (x²).(-x³).(-x) 4 = x 9

17. The value of (x – y)(x + y) + (y – z)(y + z) + (z – x) (z + x) is:

A. x + y + z

B. x² + y² + z²

C. xy + yz + zx

Answer: D. 0

(x – y)(x + y) + (y – z)(y + z) + (z – x) (z + x)

18. (a – b)² is equal to:

A. a² + b² – 2ab

B. a² + b² + 2ab

Answer: A. a² + b² – 2ab

Explanation: By algebraic identity,

(a + b)² = a² + b² – 2 ab

19. The product of 3xy 2 z and 4x is:

C. 12x 2 y 2 z

D. 12x 2 yz

Answer: C. 12x 2 y 2 z

Explanation: The product of 3xy 2 z and 4x is:

⇒ (3xy 2 z) (4x)

⇒ 3.x.y 2 .z.4.x

⇒ 12x 2 y 2 z

20. Which of the following is a like term as 8xy?

Answer: D. xy

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NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities

Subject specialists have designed NCERT solutions for Maths Class 8 Chapter 9 which includes thorough solutions for reference. These solutions are updated according to the latest CBSE syllabus for 2012-22 and are provided in easy language for understanding. Tips and tricks are also provided.

These solutions are provided so a student can clear his doubts and get help with deep understanding of the concept. Also you can refer them to make the chapter notes and revisions notes. PDF of this can also be downloaded from website.

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NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities

The NCERT Solutions of this chapter starts with basic concepts like terms, factors, coefficients, like and unlike terms, addition and subtraction of algebraic expressions, and multiplication of two or more polynomials. Students can go through the various algebraic expression identities and solve problems applying these identities. In NCERT Class 8, this chapter carries a total weightage of 8 to 10 marks in the final examination. Students can use them to solve exercise questions and preparing for their examination.

Get detailed solutions for all the questions listed under the below exercises:

: 4 Questions (Short answers)

: 5 Questions (Short answers)

: 5 Questions (Short answers) : 3 Questions (Short answers)

: 8 Questions (Short answers)

This chapter generally covers the study of solving polynomial related problems. The chapter provide a strong foundation for the students to score good marks.

The main topics covered in this chapter include:


9.1	What are Expressions?
9.2	Terms, Factors and Coefficients
9.3	Monomials, Binomials and Polynomials
9.4	Like and Unlike Terms
9.5	Addition and Subtraction of Algebraic Expressions
9.6	Multiplication of Algebraic Expressions: Introduction
9.7	Multiplying a Monomial by a Monomial
9.8	Multiplying a Monomial by a Polynomial
9.9	Multiplying a Polynomial by a Polynomial
9.10	What is an Identity?
9.11	Standard Identities
9.12	Applying Identities

Key Features of NCERT Solutions for this chapter

NCERT Solutions helps in providing fully resolved step by step solutions to all textbook questions.
Set of solutions which comes with a list of all important formulas on algebraic identities.
These solutions are made accordance to the latest syllabus.
Solutions are prepared by subject matter experts.
NCERT Solutions provides help for the preparation of competitive exams.

Frequently Asked Questions on NCERT Solutions of this Chapter

How is NCERT Solutions from this chapter helpful for board exams?

NCERT Solutions of this chapter comes with detailed descriptions as per the term limit particularised by the Board for self-evaluation. Solving these solutions can help in providing the good marks in exams. Students can improve their skills on siting on exam dah

Is it necessary to practice all the exercises present in Chapter 9 of NCERT Solutions for Class 8 Maths?

Yes. As these questions seem to be important for exam. These questions are solved by subject matter experts for helping students to crack these exercises easily. These solutions give students knowledge about data handling. Solutions can be downloaded in PDF format on INFINITE LEARN website..

Mention the topics that are covered in these NCERT Solutions?

The topics included in NCERT Solutions of this chapter are 9.1 – introduction to expressions, 9.2 – terms, factors and coefficients, 9.3 – monomials, binomials and polynomials, 9.4 – like and unlike terms, 9.5 – addition and subtraction of algebraic expressions, 9.6 – multiplication of algebraic expressions: introduction, 9.7 – multiplying a monomial by a monomial, 9.8 – multiplying a monomial by a polynomial, 9.9 – multiplying a polynomial by a polynomial, 9.10 – definition and meaning of identity, 9.11 – standard identities and 9.12 – applying identities.

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NCERT Solutions for Class 8 Maths Algebraic Expressions and Identities

NCERT Solutions for Class 8 Maths Algebraic Expressions and Identities are created by askIITians experts to help you understand all the basic concepts of the chapter. With these solutions, you can easily revise the main topics of the chapter and prepare yourself for the Class 8 final Maths examination. We have provided stepwise solutions for all the exercise questions of the chapter with comprehensive explanations. You can download the NCERT Solutions for this chapter for free in pdf form and practice its exercises whenever you want.

Chapter 9 Algebraic Expressions and Identities is an important chapter as it helps build a fundamental understanding of important concepts of algebra. The chapter includes basic definitions of expressions, terms, variables and coefficients. You will study different types of polynomial expressions such as monomials, binomials, trinomials, along with like terms, unlike terms, and addition, subtraction and multiplication of algebraic expressions.

About NCERT Class 8 Maths Chapter 9 Algebraic Expressions and Identities

Algebraic Expression: Any mathematical expression which consists of numbers, variables and operations is called an Algebraic Expression . For example, 7x + 4, 22y + 91
Terms: Every algebraic expression is made up of two or more terms . Terms are added to form expressions. Terms themselves can be formed as the product of factors. For example, the term 4x is the product of its factors 4 and x. The term 5 is made up of just one factor, i.e., 5.
Monomial: An algebraic expression with only one term is called a monomial. For example, 2x, 76y, x 2 y, etc are monomials.
Polynomial: Algebraic expressions that have more than two terms with non-zero coefficients and variables having non-negative integral exponents are called polynomials. For example, x+y+z, 2x+45y, etc are polynomials.
Binomial: An algebraic expression that includes only two terms is known as a binomial. For example, 5a 2 + 5, 3x+3y etc are binomial expressions.

(a + b) 2 = a 2 + 2ab + b 2

(a - b) 2 = a 2 - 2ab + b 2

(a + b) (a - b) = a 2 - b 2

Download Free NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities

At askIITians, you can find exercise-wise solutions for Chapter 9 Algebraic Expressions and Identities. This way you can practise the exercises at your own pace and learn independently. Our comprehensive solutions will make it easier for you to understand the important concepts of the chapter and prepare well for your exams.

Chapter 9 Class 8 Maths NCERT Ex 9.1 Solutions

The first exercise of Algebraic Expressions and Identities includes 4 questions. This exercise is based on the introduction to algebraic expressions, terms, coefficients, monomials, binomials, and polynomial expressions. It also includes questions related to like and unlike terms and addition and subtraction of algebraic expressions.

Chapter 9 Class 8 Maths NCERT Ex 9.2 Solutions

The second exercise of Algebraic Expressions and Identities includes 5 questions. This exercise is based on the introduction to the multiplication of algebraic expressions, multiplying a monomial by a monomial and multiplying three or more monomials. Make sure you practice this exercise carefully.

Chapter 9 Class 8 Maths NCERT Ex 9.3 Solutions

The third exercise of this chapter includes 5 questions. This exercise is based on multiplying a monomial by a binomial and multiplying a monomial by a trinomial. This exercise is based on exercise 9.2. So if you have understood the previous exercise, you will be able to solve its questions easily. In case you have any doubt, check our NCERT Solutions.

Chapter 9 Class 8 Maths NCERT Ex 9.4 Solutions

The fourth exercise of this chapter includes 3 questions. It is based on two important multiplication concepts - multiplication of a binomial by a binomial and multiplication of a binomial by a trinomial. This is an advanced level exercise. You must solve this exercise carefully as many students make mistakes in multiplying larger algebraic expressions.

Chapter 9 Class 8 Maths NCERT Ex 9.5 Solutions

The fifth exercise of this chapter includes 8 questions. It is based on important algebraic identities and their application. This exercise forms the basis of algebra in higher classes. So, you must practice every question of this exercise thoroughly. Our NCERT Solutions are here to guide you in case you have any doubts.

Why download NCERT Class 8 Maths Solutions for Chapter 9 Algebraic Expressions and Identities:

NCERT Solutions are free to download in pdf format so that you can refer to them whenever you need them.
The solutions include comprehensive explanations that will help in enhancing your conceptual understanding of the chapter.
Every question is solved step by step which will make exam preparation easier for you.
You can study the NCERT Solutions independently and practice the questions at your own pace.
With these NCERT Solutions, you will understand how to approach different types of questions in the exams related to algebraic expressions and identities.

NCERT Class 8 Maths Chapter 9 Algebraic Expressions and Identities FAQs

How many questions are there in NCERT Class 8 Maths Chapter 9 Algebraic Expressions and Identities?

There are 25 unsolved questions in NCERT Class 8 Maths Chapter 9 Algebraic Expressions and Identities. You can download the stepwise solutions for all these questions from the askIITians website.

I need more help in learning Chapter 9 Algebraic Expressions and Identities. What should I do?

You can find many different study resources for Class 8 Maths NCERT Chapter 9 Algebraic Expressions and Identities such as revision notes, mind maps, flashcards, extra questions, and more. We also provide online coaching for Class 8 Maths so that students can study from the best teachers of India through the safety and comfort of their homes.

What are the topics covered in NCERT Class 8 Maths Chapter 9 Algebraic Expressions and Identities?

Class 8 Maths Chapter 9 includes the basic definitions of algebraic expressions, terms, variables and coefficients. It also includes different types of polynomial expressions such as monomials, binomials, trinomials, along with like terms, unlike terms, and addition, subtraction and multiplication of algebraic expressions.

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NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities

Ncert solutions for class 8 maths chapter 9 algebraic expressions and identities| pdf download.

Exercise 9.1 Chapter 9 Class 8 Maths NCERT Solutions
Exercise 9.2 Chapter 9 Class 8 Maths NCERT Solutions
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Exercise 9.5 Chapter 9 Class 8 Maths NCERT Solutions

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How many exercises in Chapter 9 Algebraic Expressions and Identities?

Identify the variable and constant in the expression 24 – x., the length and breadth of a rectangle are 3x 2 – 2 and 2x + 5 respectively. find its area., verify the identity (x + a)( x + b) = x 2 + (a + b)x + ab for a = 2, b = 3 and x = 4,, contact form.

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Class 8 Maths MCQ Questions of Algebraic Expressions and Identities with Answers

Class 8 Maths MCQ Questions of Algebraic Expressions and Identities with Answers?

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Students must solve the important Class 8 Maths MCQ Questions of Algebraic Expressions and Identities with Answers. This will help them to keep up with what is being taught in class and what might appear in the exams. A significant chunk of questions from this subject comes within the type of MCQ Questions. Therefore, by practicing more objective-type questions, the students will ensure securing better marks from this chapter.

MCQ Questions for class 8 Maths allow the students to study in-depth and prepare well in advance. They contain only the questions which are most likely to appear in the examinations. These questions are carefully curated based on the current syllabus, and curriculum, previous year questions papers.

Practice the MCQ Questions for Class 8 Algebraic Expressions and Identities with answers which are given here.

Practice MCQ Question for Class 8 Maths chapter-wise

1. The expression x + 3 is in

(a) one variable (b) two variables (c) no variable (d) none of these

2. The value of the expression x 3 + y 3 when x=2 and y=-2 is

(a) 0 (b) 8 (c) 16 (d) -16

3. The expression 4xy + 7 is in

4. The value of 5x when x = 5 is

(a) 5 (b) 10 (c) 25 (d) -5

5. The value of x 2 – 2x + 1 when x = 1 is

(a) 1 (b) 2 (c) -2 (d) 0

6. The value of x 2 + y 2 when x = 1, y = 2 is

(a) 1 (b)2 (c) 4 (d) 5

7. The sum of 7x, 10x and 12x is

(a) 17x (b) 22x (c) 19x (d) 29x

8. The sum of 8pq and -17 pq is

(a) pq (b) 9pq (c) -9pq (d) -pq

9. The sum of 5x 2 , -7x 2 , 8x 2 , 11x 2 and -9x 2 is

(a) 2x 2 (b) 4x 2 (c) 6x 2 (d) 8x 2

10. The result of subtraction of 3x from -4x is

(a) -7x (b) 7x (c) x (d) -x

11. The product of 7x and -12x is

(a) 84x 2 (b) -84x 2 (c) x 2 (d) -x 2

12. The area of a rectangle whose length and breadth are 9y and 4y² respectively is

(a) 4y 3 (b) 9y 3 (c) 36y 3 (d) 13y 3

13. The volume of a cube of side 2a is

(a) 4a 2 (b) 2a (c) 8a 3 (d) 8

14. The algebraic expression 3x + 2y + 6 is

(a) monomial (b) Binomial (c) Trinomial (d) None of the above

15. If we add, 7xy + 5yz – 3zx, 4yz + 9zx – 4y and -3xz + 5x – 2xy, then the answer is:

(a) 5xy + 9yz + 3zx + 5x – 4y (b) 5xy – 9yz + 3zx – 5x – 4y (c) 5xy + 10yz + 3zx + 15x – 4y (d) 5xy + 10yz + 3zx + 5x – 6y

16. If we subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3, then the answer is:

(a) 8a + 2ab + 2b + 15 (b) 8a + 2ab + 2b – 15 (c) 8a – 2ab + 2b – 15 (d) 8a – 2ab – 2b – 15

17. The volume of a rectangle with length, breadth and height as 5x, 3x 2 and 7x 4 respectively is:

(a) 105x 7 (b) 105x 2 (c) 105x 4 (d) 105x

18. The area of a rectangle that has length = 2a 2 b and breadth = 3ab 2 is::

(a) 6a 3 b 3 (b) a 3 b 3 (c) 8a 3 b 3 (d) 6a 3 b 0

19. Expressions consists of _____________ and _______________.

(a) variables, constants (b) identities (c) expressions (d) none of these

20. An algebraic expression consisting of three terms is called a ______ expression.

(a) monomial (b) trinomial (c) binomial (d) polynomial

21. Value of expression a(a 2 +a +1)+5 for ‘ a’ = 0 is

(a) a+5 (b) 1 (c) 6 (d) 5

22. Identify the coefficient of xy 2 in xy – 4xy 2 – 5x 2 y

(a) -5 (b) 5 (c) -4 (d) 4

23. Obtain the volume of rectangle boxes with length, breadth and height are. 6a, 3b 2 , 7a 4

(a) 15a 3 b 5 (b) 216 b 3 (c) 126 a 5 b 2 (d) 17a 2 b 3

24. Which of the following is like term as 7xy?

(a) 9 (b) 9x (c) 9y (d) 9xy

25. If a + b + c = 9 and ab + bc + ca = 26, then the value of a 3 + b 3 + c 3 – 3abc

(a) 27 (b) 29 (c) 729 (d) 495

1. Answer: (a) one variable

Explanation: The only variable is x.

2. Answer: (a) 0

Explanation: Value of x 3 +y 3

=(2) 3 +(−2) 3

3. Answer: (b) two variables

Explanation: There are two variables x and y.

4. Answer: (c) 25

Explanation: Value = 5 × 5

5. Answer: (d) 0

Explanation: Value = (1) 2 – 2(1) + 1

6. Answer: (d) 5

Explanation: Value = (1) 2 + (2) 2

7. Answer: (d) 29x

Explanation: Sum = (7 + 10 + 12)x

8. Answer: (c) -9pq

Explanation: Sum = {8 + (-17)} pq

9. Answer: (d) 8x 2

Explanation: Sum = {5 + (-7) + 8 + 11 + (-9)} x 2

= 8x 2

10. Answer: (a) -7x

Explanation: -4x -3x

11. Answer: (b) -84x 2

Explanation: (7x) (-12x)

12. Answer: (c) 36y 3

Explanation: Area of rectangle = l x b

= (9y)(4y 2 )

13. Answer: (c) 8a 3

Explanation: Volume = 2a × 2a × 2a

14. Answer: (c) Trinomial

Explanation: The algebraic expression containing three terms is called a trinomial. Here, 3x, 2y and 6 are three terms.

15. Answer: (a) 5xy + 9yz + 3zx + 5x – 4y

Explanation: Given, 7xy + 5yz – 3zx, 4yz + 9zx – 4y and -3xz + 5x – 2xy.

If we add the three expressions, then we need to combine the like terms together.

(7xy – 2xy)+(5yz + 4yz) – 3zx + 9zx – 3xz – 4y + 5x

= 5y + 9yz + 3zx + 5x – 4y

16. Answer: (c) 8a – 2ab + 2b – 15

Explanation: (12a – 9ab + 5b – 3) – (4a – 7ab + 3b + 12)

= 12a – 9ab + 5b – 3 – 4a + 7ab – 3b – 12

= (12 – 4)a – (9 – 7)ab + (5 – 3)b – 3 – 12

= 8a – 2ab + 2b – 15

17. Answer: (a) 105x 7

Explanation: Volume of rectangle = Length × breadth × height

V = 5x × 3x 2 × 7x 4

V = 105 x 1+2+4

V = 105x 7 cubic unit.

18. Answer: (a) 6a 3 b 3

Explanation: Area of rectangle (l x b)

= (2a 2 b)(3ab 2 )

= 6a 3 b 3

19. Answer: (a) variables, constants

Explanation: An expression is a combination of operators, constants and variables. An expression may consist of one or more operands, and zero or more operators to produce a value.

20. Answer: (b) trinomial

Explanation: An algebraic Expression containing one term is monomial.

An algebraic Expression containing two terms is binomial.

An algebraic Expression containing three terms is trinomial.

21. Answer: (d) 5

Explanation: a(a 2 +a+1)+5

=a 3 +a 2 +a+5

Putting the value of a,we get,

a 3 +a 2 +a+5

22. Answer: (c) -4

Explanation: xy – 4xy 2 – 5x 2 y = 0

= (-4) xy 2

= Coefficient (-4)

23. Answer: (c) 126 a 5 b 2

Explanation: 6a × 3b 2 × 7a 2

= 6 × a × 3 × b × b × 7 × a × a

= 126 a 5 b 2

24. Answer: (d) 9xy

Explanation: The terms which have the same literal coefficients raised to the same powers but may only differ in numerical coefficient are like terms.

25. Answer: (a) 27

Explanation: ⇒ (a + b + c) 2 = 81 [On squaring both sides of (i)]

⇒ a 2 + b 2 + c 2 + 2(ab + bc + ac) = 81

⇒ a 2 + b 2 + c 2 + 2 × 26 = 81 [∵ab + bc + ac = 26]

⇒ a 2 + b 2 + c 2 = (81 - 52)

⇒ a 2 + b 2 + 2 = 29.

Now, we have

a 3 + b 3 + c 3 - 3abc = (a + b + c) (a 2 + b 2 + c 2 - ab - bc - ac)

= (a + b + c) [(a 2 + b 2 + c 2 ) - (ab + bc + ac)]

= 9 × [(29 - 26)]

= (9 × 3)

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