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# RD Sharma Solution for Class 9 Mathematics Chapter 4 - Algebraic Identities

Our RD Sharma Textbook Solutions are considered extremely helpful for solving the tough questions which are asked in the CBSE Class 9 exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 4 - Algebraic Identities.

All our solutions are created in accordance with the latest CBSE syllabus, and they are amended from time to time to provide the most relevant answers. Our free RD Sharma Solutions for CBSE Class 9 Mathematics will strengthen your fundamentals in Mathematics and will help you in your attempts to score more marks in the final examination. CBSE Class 9 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

Exercise/Page

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 1(v)

Solution 2(i)

Solution 2(ii)

Solution 2(iii)

Solution 2(iv)

Solution 3(i)

Solution 3(ii)

Solution 3(iii)

Solution 3(iv)

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10(i)

Solution 10(ii)

Solution 11

Solution 12

Solution 13(i)

Solution 13(ii)

Solution 13(iii)

Solution 13(iv)

Solution 14

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 1(v)

Solution 1(vi)

Solution 1(vii)

Solution 1(viii)

Solution 1(ix)

Solution 1 (x)

Solution 1 (xi)

Solution 1 (xii)

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6(i)

Solution 6(ii)

Solution 6(iii)

Solution 6(iv)

Solution 6(v)

Solution 7(i)

Solution 7(ii)

Solution 7(iii)

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11(i)

Solution 11(ii)

Solution 11(iii)

Solution 11(iv)

Solution 11(v)

Solution 11(vi)

Solution 12(i)

Solution 12(ii)

Solution 12(iii)

Solution 12(iv)

Solution 13

Solution 14(i)

Solution 14(ii)

Solution 15

Solution 16

Solution 17(ii)

Solution 17(iii)

Solution 17(iv)

Solution 17(i)

Solution 18

Solution 19

## RD Sharma Solution for Class 9 Mathematics Chapter 4 - Algebraic Identities Page/Excercise 4.4

Solution 1 (i)

Solution 1 (ii)

Solution 1 (iii)

Solution 1 (iv)

Solution 1 (v)

Solution 1 (vi)

Solution 1 (vii)

Solution 1 (viii)

Solution 1 (ix)

Solution 1 (x)

Solution 1 (xi)

Solution 1 (xii)

Solution 2 (i)

Solution 2 (ii)

Solution 2 (iii)

Solution 2 (iv)

Solution 2 (v)

Solution 3

Solution 4

Solution 5

Solution 6 (iii)

Solution 6 (i)

Solution 6 (ii)

Solution 1 (i)

Solution 1 (ii)

Solution 1 (iii)

Solution 1 (iv)

Solution 2(i)

Solution 2(ii)

Solution 2(iii)

Solution 2(iv)

Solution 3

Solution 4

Solution 5

## RD Sharma Solution for Class 9 Mathematics Chapter 4 - Algebraic Identities Page/Excercise 4.30

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

We know that (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

Here, a + b + c = 9, ab + bc + ca = 23

Thus, we have

(9)2 = a2 + b2 + c2 + 2(23)

81 = a2 + b2 + c2 + 46

a2 + b2 + c2 = 81 - 46

a2 + b2 + c2 = 35

Hence, correct option is (a).

Solution 9

Solution 10

Solution 11

a - b = -8

(a - b)2 = 64

a2 + b2 - 2ab = 64

a2 + b2 - 2ab + 3ab = 64 + 3ab

a2 + b2 + ab = 64 + 3(-12)

a2 + b2 + ab = 64 - 36

a2 + b2 + ab = 28

Now a3 - b3 = (a - b)(a2 + b2 + ab)

= (-8)(28)

= -224

Hence, correct option is (c).

## RD Sharma Solution for Class 9 Mathematics Chapter 4 - Algebraic Identities Page/Excercise 4.31

Solution 12

Volume of a cuboid of side a, b and c = abc

Now, Volume = 3x2 - 27    (given)

abc = 3(x2 - 9)

abc = 3(x - 3)(x + 3)

So, possible dimensions are 3, x - 3 and x + 3

Hence, correct option is (b).

Solution 13

Given expression is 75 × 75 + 2 × 75 × 25 + 25 × 25

Let 75 = a and 25 = b

Then, we have

× a + 2 × a × b + b × b

a2 + 2ab + b2

= (a + b)2

= (75 + 25)2

= (100)2

= 10000

Hence, correct option is (a).

Solution 14

(x - y)(x + y) = x2 - y2  [by identity (a + b)(a - b) = a2 - b2]

(x2 - y2)(x2 + y2) = x4 - y4

(x4 - y4)(x4 + y4) = x8 - y8

Now,

(x - y)(x + y)(x2 + y2)(x4 + y4)

= (x2 - y2)(x2 + y2)(x4 + y4)

= (x4 - y4)(x4 + y4)

= x8 - y8

Hence, correct option is (b).

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

a2 + b2 + c2 - ab - bc - ca = 0

Multiplying by 2 on both the sides, we have

2(a2 + b2 + c2 - ab - bc - ca) = 0

2a+ 2b2 + 2c2 - 2ab - 2bc - 2ca = 0

a2 + a2 + b2 + b2 + c+ c2 - 2ab - 2bc - 2ca = 0

(a2 + b2 - 2ab) + (b2 + c2 - 2bc) + (a2 + c2 - 2ac) = 0

(a - b)2 + (b - c)2 + (a - c)2 = 0

(a - b)2 = 0(b - c)2 = 0, (a - c)2 = 0

(a - b) = 0(b - c) = 0, (a - c) = 0

a = b, b = c, a = c

or we can say a = b = c

Hence, correct option is (d).

Solution 20

Solution 21

Solution 22

Given, a + b + c = 9

Hence, (a + b + c)2 = 81

So, a2 + b2 + c2 + 2ab + 2bc + 2ca = 81

i.e. a2 + b2 + c2 + 2(ab + bc + ca) = 81

i.e. a2 + b2 + c2 + 2(23) = 81

i.e. a2 + b2 + c2 = 81 - 46 = 35

Now, a3 + b3 + c3 - 3abc

= (a + b + c)(a2 + b2 + c2 - ab - bc - ca)

= (a + b + c)[(a2 + b2 + c2) - (ab + bc + ca)]

= (9)[35 - 23]

= 9 × 12

= 108

Hence, correct option is (a).

Solution 23

## RD Sharma Solution for Class 9 Mathematics Chapter 4 - Algebraic Identities Page/Excercise 4.32

Solution 24

Solution 25

Given expression is (x2 - 1)(x4 + x2 + 1)

Let x2 = A and 1 = B

Then, we have

(A - B)(A2 + AB + B2)

= A3 - B3

= (x2)3 - (1)3

= x6 - 1

Hence, correct option is (c).

Solution 26

Solution 27

## Browse Study Material

TopperLearning provides step-by-step solutions for each question in each chapter in the RD Sharma textbook for class 9. Access the CBSE Class 9 Mathematics Chapter 4 - Algebraic Identities for free. The textbook questions have been solved by our subject matter experts to help you understand how to answer them. Our RD Sharma Textbook Solutions will help you to study and revise, and you can easily clear your fundamentals of Chapter 4 - Algebraic Identities.

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CBSE IX - Mathematics

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