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

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RD Sharma solutions for Mathematics for Class 9 chapter 5 - Factorisation of Algebraic Expressions - Shaalaa.com
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Solutions for Chapter 5: Factorisation of Algebraic Expressions

Below listed, you can find solutions for Chapter 5 of CBSE RD Sharma for Mathematics for Class 9.


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

Solutions for 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 - Shaalaa.com

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

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

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

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

Using RD Sharma Mathematics for Class 9 solutions Factorisation of Algebraic Expressions exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in RD Sharma Solutions are essential questions that can be asked in the final exam. Maximum CBSE Mathematics for Class 9 students prefer RD Sharma Textbook Solutions to score more in exams.

Get the free view of Chapter 5, Factorisation of Algebraic Expressions Mathematics for Class 9 additional questions for Mathematics Mathematics for Class 9 CBSE, and you can use Shaalaa.com to keep it handy for your exam preparation.

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