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

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## Chapter 5: Factorisation of Algebraic Expressions

Ex. 5.1Ex. 5.2Ex. 5.3Ex. 5.4Others

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

Ex. 5.1 | Q 1 | Page 9

Factorize: x3 + x - 3x2 - 3

Ex. 5.1 | Q 2 | Page 9

Factorize: a (a + b)3 - 3a2b (a + b)

Ex. 5.1 | Q 3 | Page 9

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

Ex. 5.1 | Q 4 | Page 9

Factorize: a^2 x^2 + (ax^2 + 1)x + a

Ex. 5.1 | Q 5 | Page 9

Factorize : x2 + y - xy - x

Ex. 5.1 | Q 6 | Page 9

Factorize x3 - 2x2 y + 3xy2 - 6y3

Ex. 5.1 | Q 7 | Page 9

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

Ex. 5.1 | Q 8 | Page 9

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

Ex. 5.1 | Q 9 | Page 9

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

Ex. 5.1 | Q 10 | Page 9

Factorize a2 + 2ab + b2 - c2

Ex. 5.1 | Q 11 | Page 9

Factorize  a2 + 4b2 - 4ab - 4c2

Ex. 5.1 | Q 12 | Page 9

Factorize x2 - y2 - 4xz + 4z2

Ex. 5.1 | Q 13 | Page 9

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

Ex. 5.1 | Q 14 | Page 9

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

Ex. 5.1 | Q 15 | Page 9

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

Ex. 5.1 | Q 16 | Page 9

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

Ex. 5.1 | Q 17 | Page 9

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

Ex. 5.1 | Q 18 | Page 9

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

Ex. 5.1 | Q 19 | Page 9

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

Ex. 5.1 | Q 20 | Page 9

Factorize 2a^2 + 2  sqrt6ab + 3b^2

Ex. 5.1 | Q 21 | Page 9

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

Ex. 5.1 | Q 22 | Page 9

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

Ex. 5.1 | Q 23 | Page 9

Factorize a2 - b2 + 2bc - c2

Ex. 5.1 | Q 24 | Page 9

Factorize xy9 - yx9

Ex. 5.1 | Q 25 | Page 9

Factorize x4 + x2 y2 + y4

Ex. 5.1 | Q 26 | Page 9

Factorize x^2 + 6sqrt2x + 10

Ex. 5.1 | Q 27 | Page 9

Factorize x^2 - 2sqrt2x - 30

Ex. 5.1 | Q 28 | Page 9

Factorize x^2 - sqrt3x - 6

Ex. 5.1 | Q 29 | Page 9

Factorize x^2 + 5sqrt5x + 30

Ex. 5.1 | Q 30 | Page 9

Factorize x^2 + 2sqrt3x - 24

Ex. 5.1 | Q 31 | Page 9

Factorize 5sqrt5x^2 + 20x + 3sqrt5

Ex. 5.1 | Q 32 | Page 9

Factorize 2x^2 + 3sqrt5x + 5

Ex. 5.1 | Q 33 | Page 9

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

Ex. 5.1 | Q 34 | Page 9

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

Ex. 5.1 | Q 35 | Page 9

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

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

Ex. 5.2 | Q 1 | Page 14

Factorize the following expressions:

p3 + 27

Ex. 5.2 | Q 2 | Page 14

Factorize the following expressions:

y3 +125

Ex. 5.2 | Q 3 | Page 14

Factorize the following expressions

1- 27a3

Ex. 5.2 | Q 4 | Page 14

Factorize the following expressions

8x3 y3 + 27a3

Ex. 5.2 | Q 5 | Page 14

Factorize the following expressions

64a3 – b3

Ex. 5.2 | Q 6 | Page 14

Factorize the following expressions:

x^3/216 - 8y^3

Ex. 5.2 | Q 7 | Page 14

Factorize the following expressions:

10x4y – 10xy4

Ex. 5.2 | Q 8 | Page 14

Factorize the following expressions:

54x6y + 2x3y4

Ex. 5.2 | Q 9 | Page 14

Factorize the following expressions:

32a3 + 108b3

Ex. 5.2 | Q 10 | Page 14

Factorize the following expressions:

(a - 2b)3 - 512b3

Ex. 5.2 | Q 11 | Page 14

Factorize the following expressions:

8x^2y^3 - x^5

Ex. 5.2 | Q 12 | Page 14

Factorize the following expressions:

1029 – 3x3

Ex. 5.2 | Q 13 | Page 14

Factorize the following expressions:

x3y3 + 1

Ex. 5.2 | Q 14 | Page 14

Factorize the following expressions:

x4y4 - xy

Ex. 5.2 | Q 15 | Page 14

Factorize the following expressions:

a3 + b3 + a + b

Ex. 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)

Ex. 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)

Ex. 5.2 | Q 16.3 | Page 14

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

Ex. 5.2 | Q 17 | Page 14

Factorize the following expressions:

(a + b)3 – 8(a – b)3

Ex. 5.2 | Q 18 | Page 14

Factorize the following expressions:

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

Ex. 5.2 | Q 19 | Page 14

Factorize the following expressions:

x6 + y6

Ex. 5.2 | Q 20 | Page 14

Factorize the following expressions:

a12 + b12

Ex. 5.2 | Q 21 | Page 14

Factorize the following expressions:

x3 + 6x2 +12x +16

Ex. 5.2 | Q 22 | Page 14

Factorize the following expressions:

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

Ex. 5.2 | Q 23 | Page 14

Factorize the following expressions:

a3 + 3a2b + 3ab2 + b3 - 8

Ex. 5.2 | Q 24 | Page 14

Factorize the following expressions:

8a3 - b3 - 4ax + 2bx

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

Ex. 5.3 | Q 1 | Page 17

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

Ex. 5.3 | Q 2 | Page 17

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

Ex. 5.3 | Q 3 | Page 17

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

Ex. 5.3 | Q 4 | Page 17

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

Ex. 5.3 | Q 5 | Page 17

Factorize  a3 – 3a2b + 3ab2 – b3 + 8

Ex. 5.3 | Q 6 | Page 17

Factorize  x3 + 8y3 + 6x2 y +12xy2

Ex. 5.3 | Q 7 | Page 17

Factorize  8x2 + y3 +12x2 y + 6xy2

Ex. 5.3 | Q 8 | Page 17

Factorize 8a3 + 27b3 + 36a2b + 54ab2

Ex. 5.3 | Q 9 | Page 17

Factorize  8a3 – 27b3 – 36a2b + 54ab2

Ex. 5.3 | Q 10 | Page 17

Factorize  x3  -12x ( x - 4) - 64

Ex. 5.3 | Q 11 | Page 17

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

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

Ex. 5.4 | Q 1 | Page 23

a3 + 8b3 + 64c3 - 24abc

Ex. 5.4 | Q 2 | Page 23

x3 - 8y3 + 27z3 +18xyz

Ex. 5.4 | Q 3 | Page 23

27x3 − y3 − z3 − 9xyz

Ex. 5.4 | Q 4 | Page 23

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

Ex. 5.4 | Q 5 | Page 23

8x3 + 27y3 - 216z3 + 108xyz

Ex. 5.4 | Q 6 | Page 23

125 + 8x3 - 27 y3 + 90xy

Ex. 5.4 | Q 7 | Page 23

8x3 -125y3 +180xy + 216

Ex. 5.4 | Q 8.1 | Page 23

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

Ex. 5.4 | Q 8.2 | Page 23

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

Ex. 5.4 | Q 8.3 | Page 23

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

Ex. 5.4 | Q 8.4 | Page 23

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

Ex. 5.4 | Q 9 | Page 23

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

Ex. 5.4 | Q 10 | Page 23

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

Ex. 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

Ex. 5.4 | Q 12 | Page 23

(a – 3b)3 + (3b – c)3 + (c – a)3

Ex. 5.4 | Q 13 | Page 23

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

Ex. 5.4 | Q 14 | Page 23

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

Ex. 5.4 | Q 15 | Page 23

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

Ex. 5.4 | Q 16 | Page 23

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

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

Q 1 | Page 24

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

Q 2 | Page 24

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

Q 3 | Page 24

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

Q 4 | Page 24

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

Q 5 | Page 24

Write the value of 253 − 75+ 503.

Q 6 | Page 24

Write the value of 483 − 303 − 183.

Q 7 | Page 24

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

Q 8 | Page 24

Write the value of 303 + 203 − 503.

Q 9 | Page 25

Factorize: x4 + x2 + 25.

Q 10 | Page 25

Factorize : x2 − 1 − 2a − a2

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

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)

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)

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)

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

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)

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

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

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

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

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

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)

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)

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

Q 14 | Page 26

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

• 1

• 2

• 4

• 8

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

Ex. 5.1Ex. 5.2Ex. 5.3Ex. 5.4Others

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

RD Sharma solutions for Mathematics for Class 9 chapter 5 (Factorisation of Algebraic Expressions) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 9 solutions in a manner that help students grasp basic concepts better and faster.

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

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