# RD Sharma solutions for Mathematics for Class 9 chapter 5 - Factorisation of Algebraic Expressions [Latest edition]

## Chapter 5: Factorisation of Algebraic Expressions

Exercise 5.1Exercise 5.2Exercise 5.3Exercise 5.4Exercise 5.5Exercise 5.6
Exercise 5.1 [Page 9]

### RD Sharma solutions for Mathematics for Class 9 Chapter 5 Factorisation of Algebraic Expressions Exercise 5.1 [Page 9]

Exercise 5.1 | Q 1 | Page 9

Factorize: x3 + x - 3x2 - 3

Exercise 5.1 | Q 2 | Page 9

Factorize: a (a + b)3 - 3a2b (a + b)

Exercise 5.1 | Q 3 | Page 9

Factorize x (x3 - y3 ) + 3xy ( x - y )

Exercise 5.1 | Q 4 | Page 9

Factorize: a^2 x^2 + (ax^2 + 1)x + a

Exercise 5.1 | Q 5 | Page 9

Factorize : x2 + y - xy - x

Exercise 5.1 | Q 6 | Page 9

Factorize x3 - 2x2 y + 3xy2 - 6y3

Exercise 5.1 | Q 7 | Page 9

Factorize 6ab - b^2 + 12ac - 2bc

Exercise 5.1 | Q 8 | Page 9

Factorize x( x - 2)( x - 4) + 4x - 8

Exercise 5.1 | Q 9 | Page 9

Factorize (a - b + c)2 + (b - c + a)2 + 2(a - b + c) (b - c + a)

Exercise 5.1 | Q 10 | Page 9

Factorize a2 + 2ab + b2 - c2

Exercise 5.1 | Q 11 | Page 9

Factorize  a2 + 4b2 - 4ab - 4c2

Exercise 5.1 | Q 12 | Page 9

Factorize x2 - y2 - 4xz + 4z2

Exercise 5.1 | Q 13 | Page 9

Factorize 2x^2 - 5/6x + 1/12

Exercise 5.1 | Q 14 | Page 9

Factorize x^2 + 12/35 x + 1/35

Exercise 5.1 | Q 15 | Page 9

Factorize 21x^2 - 2x + 1/21

Exercise 5.1 | Q 16 | Page 9

Given possible expressions for the length and breadth of the rectangle having 35y2 + 13y – 12 as its area.

Exercise 5.1 | Q 17 | Page 9

What are the possible expressions for the dimensions of the cuboid whose volume is 3x2 - 12x.

Exercise 5.1 | Q 18 | Page 9

Factorize [x^2 + 1/x^2] - 4[x + 1/x] + 6

Exercise 5.1 | Q 19 | Page 9

Factorize (x + 2)(x2 + 25) -10x2 - 20x

Exercise 5.1 | Q 20 | Page 9

Factorize 2a^2 + 2  sqrt6ab + 3b^2

Exercise 5.1 | Q 21 | Page 9

Factorize: a2  + b2  + 2 (ab + bc + ca)

Exercise 5.1 | Q 22 | Page 9

Factorize 4( x - y)2  -12( x - y)( x + y ) + 9(x + y )2

Exercise 5.1 | Q 23 | Page 9

Factorize a2 - b2 + 2bc - c2

Exercise 5.1 | Q 24 | Page 9

Factorize xy9 - yx9

Exercise 5.1 | Q 25 | Page 9

Factorize x4 + x2 y2 + y4

Exercise 5.1 | Q 26 | Page 9

Factorize x^2 + 6sqrt2x + 10

Exercise 5.1 | Q 27 | Page 9

Factorize x^2 - 2sqrt2x - 30

Exercise 5.1 | Q 28 | Page 9

Factorize x^2 - sqrt3x - 6

Exercise 5.1 | Q 29 | Page 9

Factorize x^2 + 5sqrt5x + 30

Exercise 5.1 | Q 30 | Page 9

Factorize x^2 + 2sqrt3x - 24

Exercise 5.1 | Q 31 | Page 9

Factorize 5sqrt5x^2 + 20x + 3sqrt5

Exercise 5.1 | Q 32 | Page 9

Factorize 2x^2 + 3sqrt5x + 5

Exercise 5.1 | Q 33 | Page 9

Factorize 9(2a - b)^2 - 4(2a - b) - 13

Exercise 5.1 | Q 34 | Page 9

Factorize 7(x - 2y)^2 - 25(x - 2y) + 12

Exercise 5.1 | Q 35 | Page 9

Factorize 2( x + y)2 - 9( x + y) - 5

Exercise 5.2 [Page 14]

### RD Sharma solutions for Mathematics for Class 9 Chapter 5 Factorisation of Algebraic Expressions Exercise 5.2 [Page 14]

Exercise 5.2 | Q 1 | Page 14

Factorize the following expressions:

p3 + 27

Exercise 5.2 | Q 2 | Page 14

Factorize the following expressions:

y3 +125

Exercise 5.2 | Q 3 | Page 14

Factorize the following expressions

1- 27a3

Exercise 5.2 | Q 4 | Page 14

Factorize the following expressions

8x3 y3 + 27a3

Exercise 5.2 | Q 5 | Page 14

Factorize the following expressions

64a3 – b3

Exercise 5.2 | Q 6 | Page 14

Factorize the following expressions:

x^3/216 - 8y^3

Exercise 5.2 | Q 7 | Page 14

Factorize the following expressions:

10x4y – 10xy4

Exercise 5.2 | Q 8 | Page 14

Factorize the following expressions:

54x6y + 2x3y4

Exercise 5.2 | Q 9 | Page 14

Factorize the following expressions:

32a3 + 108b3

Exercise 5.2 | Q 10 | Page 14

Factorize the following expressions:

(a - 2b)3 - 512b3

Exercise 5.2 | Q 11 | Page 14

Factorize the following expressions:

8x^2y^3 - x^5

Exercise 5.2 | Q 12 | Page 14

Factorize the following expressions:

1029 – 3x3

Exercise 5.2 | Q 13 | Page 14

Factorize the following expressions:

x3y3 + 1

Exercise 5.2 | Q 14 | Page 14

Factorize the following expressions:

x4y4 - xy

Exercise 5.2 | Q 15 | Page 14

Factorize the following expressions:

a3 + b3 + a + b

Exercise 5.2 | Q 16.1 | Page 14

Simplify (173 xx 173 xx 173 xx 127 xx 127 xx 127)/(173 xx 173 xx 173 xx 127 xx 127 xx 127)

Exercise 5.2 | Q 16.2 | Page 14

Simplify (155 xx 155 xx 155 - 55 xx 55 xx 55)/(155 xx 155 + 155 xx 55 + 55 xx 55)

Exercise 5.2 | Q 16.3 | Page 14

Simplify :  $\frac{1 . 2 \times 1 . 2 \times 1 . 2 - 0 . 2 \times 0 . 2 \times 0 . 2}{1 . 2 \times 1 . 2 + 1 . 2 \times 0 . 2 + 0 . 2 \times 0 . 2}$

Exercise 5.2 | Q 17 | Page 14

Factorize the following expressions:

(a + b)3 – 8(a – b)3

Exercise 5.2 | Q 18 | Page 14

Factorize the following expressions:

( x + 2)3 + ( x - 2)3

Exercise 5.2 | Q 19 | Page 14

Factorize the following expressions:

x6 + y6

Exercise 5.2 | Q 20 | Page 14

Factorize the following expressions:

a12 + b12

Exercise 5.2 | Q 21 | Page 14

Factorize the following expressions:

x3 + 6x2 +12x +16

Exercise 5.2 | Q 22 | Page 14

Factorize the following expressions:

a^3 - 1/a^3 - 2a + 2/a

Exercise 5.2 | Q 23 | Page 14

Factorize the following expressions:

a3 + 3a2b + 3ab2 + b3 - 8

Exercise 5.2 | Q 24 | Page 14

Factorize the following expressions:

8a3 - b3 - 4ax + 2bx

Exercise 5.3 [Page 17]

### RD Sharma solutions for Mathematics for Class 9 Chapter 5 Factorisation of Algebraic Expressions Exercise 5.3 [Page 17]

Exercise 5.3 | Q 1 | Page 17

Factorize 64a3 +125b3 + 240a2b + 300ab2

Exercise 5.3 | Q 2 | Page 17

Factorize 125x3 - 27 y3 - 225x2 y +135xy2

Exercise 5.3 | Q 3 | Page 17

Factorize 8/27 x^3 + 1 + 4/3 x^2 + 2x

Exercise 5.3 | Q 4 | Page 17

Factorize 8x3 + 27 y3 + 36x2 y + 54xy2

Exercise 5.3 | Q 5 | Page 17

Factorize  a3 – 3a2b + 3ab2 – b3 + 8

Exercise 5.3 | Q 6 | Page 17

Factorize  x3 + 8y3 + 6x2 y +12xy2

Exercise 5.3 | Q 7 | Page 17

Factorize  8x2 + y3 +12x2 y + 6xy2

Exercise 5.3 | Q 8 | Page 17

Factorize 8a3 + 27b3 + 36a2b + 54ab2

Exercise 5.3 | Q 9 | Page 17

Factorize  8a3 – 27b3 – 36a2b + 54ab2

Exercise 5.3 | Q 10 | Page 17

Factorize  x3  -12x ( x - 4) - 64

Exercise 5.3 | Q 11 | Page 17

Factorize  a3 x3 - 3a2bx2 + 3ab2 x - b3

Exercise 5.4 [Page 23]

### RD Sharma solutions for Mathematics for Class 9 Chapter 5 Factorisation of Algebraic Expressions Exercise 5.4 [Page 23]

Exercise 5.4 | Q 1 | Page 23

a3 + 8b3 + 64c3 - 24abc

Exercise 5.4 | Q 2 | Page 23

x3 - 8y3 + 27z3 +18xyz

Exercise 5.4 | Q 3 | Page 23

27x3 − y3 − z3 − 9xyz

Exercise 5.4 | Q 4 | Page 23

1/27 x^3 - y^3 + 125z^3 + 5xyz

Exercise 5.4 | Q 5 | Page 23

8x3 + 27y3 - 216z3 + 108xyz

Exercise 5.4 | Q 6 | Page 23

125 + 8x3 - 27 y3 + 90xy

Exercise 5.4 | Q 7 | Page 23

8x3 -125y3 +180xy + 216

Exercise 5.4 | Q 8.1 | Page 23

Multiply: x2 + y2 + z2 − xy + xz + yz by x + y − z

Exercise 5.4 | Q 8.2 | Page 23

Multiply: x2 + 4y2 + z3 + 2xy + xz − 2yz   by x − 2y −

Exercise 5.4 | Q 8.3 | Page 23

Multiply:  x2 + 4y2 + 2xy − 3x + 6y + 9 by x − 2y + 3

Exercise 5.4 | Q 8.4 | Page 23

Multiply: 9x2 + 25y2 + 15xy + 12x − 20y + 16 by 3x − 5y + 4

Exercise 5.4 | Q 9 | Page 23

(3x - 2 y)3 + (2 y - 4z )3 + (4z - 3x)3

Exercise 5.4 | Q 10 | Page 23

(2x - 3y)3 + (4z - 2x)3 + (3y - 4z )3

Exercise 5.4 | Q 11 | Page 23

(x/2 + y + z/3)^3 + (x/2 + (2y)/3 + z)^3 + (-(5x)/6 - y/3 - (4z)/3)^3

Exercise 5.4 | Q 12 | Page 23

(a – 3b)3 + (3b – c)3 + (c – a)3

Exercise 5.4 | Q 13 | Page 23

2sqrt2a^3 + 3sqrt3b^3 + c^3 - 3 sqrt6abc

Exercise 5.4 | Q 14 | Page 23

3sqrt3a^3 - b^3 - 5sqrt5c^3 - 3sqrt15abc

Exercise 5.4 | Q 15 | Page 23

2sqrt2a^3 + 16sqrt2b^3 + c^3 - 12abc

Exercise 5.4 | Q 16 | Page 23

Find the value of x3 + y3 − 12xy + 64, when x + y =−4

Exercise 5.5 [Pages 24 - 25]

### RD Sharma solutions for Mathematics for Class 9 Chapter 5 Factorisation of Algebraic Expressions Exercise 5.5 [Pages 24 - 25]

Exercise 5.5 | Q 1 | Page 24

If a + b + c = 0, then write the value of a3 + b3 + c3.

Exercise 5.5 | Q 2 | Page 24

If a2 + b2 + c2 = 20 and a + b + c = 0, find ab + bc + ca.

Exercise 5.5 | Q 3 | Page 24

If a + b + c = 9 and ab + bc + ca = 40, find a2 + b2 +c2.

Exercise 5.5 | Q 4 | Page 24

If a2 + b2 + c2 = 250 and ab + bc + ca = 3, find a + b + c.

Exercise 5.5 | Q 5 | Page 24

Write the value of 253 − 75+ 503.

Exercise 5.5 | Q 6 | Page 24

Write the value of 483 − 303 − 183.

Exercise 5.5 | Q 7 | Page 24

Write the value of $\left( \frac{1}{2} \right)^3 + \left( \frac{1}{3} \right)^3 - \left( \frac{5}{6} \right)^3 .$

Exercise 5.5 | Q 8 | Page 24

Write the value of 303 + 203 − 503.

Exercise 5.5 | Q 9 | Page 25

Factorize: x4 + x2 + 25.

Exercise 5.5 | Q 10 | Page 25

Factorize : x2 − 1 − 2a − a2

Exercise 5.6 [Pages 25 - 26]

### RD Sharma solutions for Mathematics for Class 9 Chapter 5 Factorisation of Algebraic Expressions Exercise 5.6 [Pages 25 - 26]

Exercise 5.6 | Q 1 | Page 25

The factors of x3 −x2y − xy2 + y3 are

• (x + y) (x2 − xy + y2)

• (x + y) (x2 + xy + y2)

• (x + y)2 (x − y)

• (x − y)2 (x + y)

Exercise 5.6 | Q 2 | Page 25

The factors of x3 − 1 + y3 + 3xy are

• (x − 1 + y) (x2 + 1 + y2 + x + y − xy)

• (x + y + 1) (x2 + y2 + 1 −xy − x − y)

•  (x − 1 + y) (x2 − 1 − y2 + x + y + xy)

• 3(x + y −1) (x2 + y2 − 1)

Exercise 5.6 | Q 3 | Page 25

The factors of 8a3 + b3 − 6ab + 1 are

• (2a + b − 1) (4a2 + b2 + 1 − 3ab − 2a)

•  (2a − b + 1) (4a2 + b2 − 4ab + 1 − 2a + b)

• (2a + b + 1) (4a2 + b2 + 1 −2ab − b − 2a)

• (2a − 1 + b) (4a2 + 1 − 4a − b − 2ab)

Exercise 5.6 | Q 4 | Page 25

(x + y)3 − (x − y)3 can be factorized as

• 2y (3x2 + y2)

• 2x (3x2 + y2)

• 2y (3y2 + x2)

• 2x (x2+ 3y2

Exercise 5.6 | Q 5 | Page 25

The expression (a − b)3 + (− c)3 + (c −a)3 can be factorized as

•  (a − b) (b − c) (c −a)

•  3(a − b) (b − c) (c −a)

• −3(a − b) (b −c) (c − a)

• (a + b + c) (a2 + b2 + c2 − ab − bc − ca)

Exercise 5.6 | Q 6 | Page 25

The value of $\frac{(2 . 3 )^3 - 0 . 027}{(2 . 3 )^2 + 0 . 69 + 0 . 09}$

• 2

• 3

• 2.327

• 2.273

Exercise 5.6 | Q 7 | Page 25

The value of $\frac{(0 . 013 )^3 + (0 . 007 )^3}{(0 . 013 )^2 - 0 . 013 \times 0 . 007 + (0 . 007 )^2}$ is

• 0.006

• 0.02

•  0.0091

•  0.00185

Exercise 5.6 | Q 8 | Page 26

Mark the correct alternative in each of the following: The factors of a2 − 1 − 2x − x2 are

• (a − x + 1) (a − x − 1)

• (a + x − 1) (a − x + 1)

•  (a+x+1)(a- x -1)

• none of these

Exercise 5.6 | Q 9 | Page 26

The factors of x4 + x2 + 25 are

• (x2 + 3x + 5) (x2 − 3x + 5)

• (x2 + 3x + 5) (x2 + 3x − 5)

• (x2 + +5) (x2 − x + 5)

• none of these

Exercise 5.6 | Q 10 | Page 26

The factors of x2 + 4y2 + 4y − 4xy − 2x − 8 are

• (x − 2y −4) (x − 2y + 2)

• (x − y + 2) (x − 4y − 4)

• (x + 2y − 4) (x + 2y + 2)

• none of these

Exercise 5.6 | Q 11 | Page 26

The factors of x3 − 7x + 6 are

• x (x − 6) (x − 1)

• (x2 − 6) (x − 1)

• (x + 1) (x + 2) (x + 3)

• (x − 1) (x + 3) (x − 2)

Exercise 5.6 | Q 12 | Page 26

The expression x4 + 4 can be factorized as

• (x2 + 2x + 2) (x2 − 2x + 2)

• (x2 + 2x + 2) (x2 + 2x + 2)

• (x2 − 2x − 2) (x2 − 2x + 2)

• (x2 + 2) (x2 − 2)

Exercise 5.6 | Q 13 | Page 26

If 3x = a + b + c, then the value of (x − a)3 + (x −b)3 + (x − c)3 − 3(x − a) (x − b) (x −c) is

• a + b + c

• (a − b) (b − c) (c − a)

• 0

• none of these

Exercise 5.6 | Q 14 | Page 26

If (x + y)3 − (x − y)3 − 6y(x2 − y2) = ky2, then k =

• 1

• 2

• 4

• 8

Exercise 5.6 | Q 15 | Page 26

If x3 − 3x2 + 3x − 7 = (x + 1) (ax2 + bx + c), then a + b + c =

• 4

• 12

• -10

• 3

## Chapter 5: Factorisation of Algebraic Expressions

Exercise 5.1Exercise 5.2Exercise 5.3Exercise 5.4Exercise 5.5Exercise 5.6

## RD Sharma solutions for Mathematics for Class 9 chapter 5 - Factorisation of Algebraic Expressions

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Concepts covered in Mathematics for Class 9 chapter 5 Factorisation of Algebraic Expressions are Algebraic Expressions.

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