# SELINA Solutions for Class 9 Maths Chapter 5 - Factorisation

Revise the different methods of factorisation with TopperLearning’s Selina Solutions for ICSE Class 9 Mathematics Chapter 5 Factorisation online. While trying to solve factorisation problems, explore our chapter solutions and learn the application of methods like splitting of the middle terms, grouping and more.

You can also revise problems based on factorisation by taking out the common factors when you practise with our Selina textbook solutions for ICSE Class 9 Maths. You may also use our Frank solutions to practise more problems - ensuring you have sufficient revised and feel confident. Also, browse through our other e-learning resources like practice tests, sample papers and more.

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## Chapter 5 - Factorisation Exercise Ex. 5(E)

Question 1

Factorize :

Solution 1

Question 2

Factorize :

Solution 2

Question 3

Factorize :

Solution 3

Question 4

Factorize :

Solution 4

Question 5

Factorize :

4x4 + 9y4 + 11x2y2

Solution 5

Question 6

Factorize :

Solution 6

Question 7

Factorize :

a - b - 4a2 + 4b2

Solution 7

Question 8

Factorize :

(2a - 3)2 - 2 (2a - 3) (a - 1) + (a - 1)2

Solution 8

Question 9

Factorize :

(a2 - 3a) (a2 + 3a + 7) + 10

Solution 9

Question 10

Factorize :

(a2 - a) (4a2 - 4a - 5) - 6

Solution 10

Question 11

Factorize :

x4 + y4 - 3x2y2

Solution 11

Question 12

Factorize :

5a2 - b2 - 4ab + 7a - 7b

Solution 12

Question 13

Factorize :

12(3x - 2y)2 - 3x + 2y - 1

Solution 13

Question 14

Factorize :

4(2x - 3y)2 - 8x+12y - 3

Solution 14

Question 15

Factorize :

3 - 5x + 5y - 12(x - y)2

Solution 15

Question 16

9x 2 + 3x - 8y - 64y2

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

2(ab + cd) - a2 - b2 + c2 + d2

Solution 19

Question 20

Solution 20

## Chapter 5 - Factorisation Exercise Ex. 5(A)

Question 1

Factorise by taking out the common factors:

2 (2x - 5y) (3x + 4y) - 6 (2x - 5y) (x - y)

Solution 1

Taking (2x - 5y) common from both terms

= (2x - 5y)[2(3x + 4y) - 6(x - y)]

=(2x - 5y)(6x + 8y - 6x + 6y)

=(2x - 5y)(8y + 6y)

=(2x - 5y)(14y)

=(2x - 5y)14y

Question 2

Factories by taking out common factors:

xy(3x2 - 2y2) - yz(2y2 - 3x2) + zx(15x2 - 10y2)

Solution 2

xy(3x2 - 2y2) - yz(2y2 - 3x2) + zx(15x2 - 10y2)

= xy(3x2 - 2y2) + yz(3x2 - 2y2) + zx(15x2 - 10y2)

= xy(3x2 - 2y2) + yz(3x2 - 2y2) + 5zx(3x2 - 2y2)

= (3x2 - 2y2)[xy + yz + 5zx]

Question 3

Factories by taking out common factors:

ab(a2 + b2 - c2) - bc(c2 - a2 - b2) + ca(a2 + b2 - c2)

Solution 3

ab(a2 + b2 - c2) - bc(c2 - a2 - b2) + ca(a2 + b2 - c2)

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

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

Question 4

Factories by taking out common factors:

2x(a - b) + 3y(5a - 5b) + 4z(2b - 2a)

Solution 4

2x(a - b) + 3y(5a - 5b) + 4z(2b - 2a)

= 2x(a - b) + 15y(a - b) - 8z(a - b)

= (a - b)[2x + 15y - 8z]

Question 5

Factorize by the grouping method:

a3 + a - 3a2 - 3

Solution 5

a3 + a - 3a2 - 3= a (a2 + 1) - 3(a2 + 1)

= (a2 + 1) (a -3).

Question 6

Factorize by the grouping method:

16 (a + b)2 - 4a - 4b

Solution 6

16 (a + b)2 - 4a - 4b =16 (a + b)2 - 4 (a + b)

= 4 (a + b) [4 (a + b) - 1]

= 4 (a + b) (4a + 4b - 1)

Question 7

Factorize by the grouping method:

a4 - 2a3 - 4a + 8

Solution 7

Question 8

Factorize by the grouping method:

ab - 2b + a2 - 2a

Solution 8

Question 9

Factorize by the grouping method:

ab (x2 + 1) + x (a2 + b2)

Solution 9

Question 10

Factorize by the grouping method:

a2 + b - ab - a

Solution 10

Question 11

Factorize by the grouping method:

(ax + by)2 + (bx - ay)2

Solution 11

Question 12

Factorize by the grouping method:

a2x2 + (ax2 + 1) x + a

Solution 12

Question 13

Factorize by the grouping method:

(2a-b)2 -10a + 5b

Solution 13

Question 14

Factorize by the grouping method:

a (a -4) - a + 4

Solution 14

Question 15

Factorize by the grouping method:

y2 - (a + b) y + ab

Solution 15

Question 16

Factorize by the grouping method:

Solution 16

Question 17

Factorise using the grouping method:

x2 + y2 + x + y + 2xy

Solution 17

= (x2 + y2 + 2xy ) + (x + y)

[As (x + y)2 = x2 + 2xy + y2]

=(x + y)2 + (x + y)

=(x + y)(x + y + 1)

Question 18

Factorise using the grouping method:

a2 + 4b2 - 3a + 6b - 4ab

Solution 18

= a2 + 4b2 - 4ab - 3a + 6b

= a2 + (2b)2 - 2 × a × (2b) - 3(a - 2b)

[As (a - b)2 = a2 - 2ab + b2 ]

=(a - 2b)2 - 3(a - 2b)

=(a - 2b)[(a - 2b)- 3]

=(a - 2b)(a - 2b - 3)

Question 19

Factorise using the grouping method:

m (x - 3y)2 + n (3y - x) + 5x - 15y

Solution 19

= m (x - 3y)2 - n (x - 3y) + 5(x - 3y)

[Taking (x - 3y) common from all the three terms]

=(x - 3y) [m(x - 3y) - n + 5]

=(x - 3y)(mx - 3my - n + 5)

Question 20

Factorise using the grouping method:

x (6x - 5y) - 4 (6x - 5y)2

Solution 20

=(6x - 5y)[x - 4(6x - 5y)]

[Taking (6x - 5y) common from the three terms]

= (6x - 5y)(x - 24x + 20y)

= (6x - 5y)(-23x + 20y)

= (6x - 5y)(20y - 23x)

## Chapter 5 - Factorisation Exercise Ex. 5(B)

Question 1

Factorize:

a2 + 10a + 24

Solution 1

Question 2

Factorize:

a2 - 3a - 40

Solution 2

Question 3

Factorize:

1 - 2a - 3a2

Solution 3

Question 4

Factorize:

x2 - 3ax - 88a2

Solution 4

Question 5

Factorize:

6a2 - a-15

Solution 5

Question 6

Factorize:

24a3 + 37a2 - 5a

Solution 6

Question 7

Factorize:

a(3a - 2) - 1

Solution 7

Question 8

Factorize:

a2b2 + 8ab - 9

Solution 8

Question 9

Factorize:

3 - a (4 + 7a)

Solution 9

Question 10

Factorize:

(2a + b)2 - 6a - 3b - 4

Solution 10

Question 11

Factorize:

1 - 2 (a+ b) - 3 (a + b)2

Solution 11

Question 12

Factorize:

3a2 - 1 - 2a

Solution 12

Question 13

Factorize:

x2 + 3x + 2 + ax + 2a

Solution 13

Question 14

Factorize:

(3x - 2y)2 + 3 (3x - 2y) - 10

Solution 14

Question 15

Factorize:

5 - (3a2 - 2a) (6 - 3a2 + 2a)

Solution 15

Question 16

Solution 16

Question 17

Factories: (x2 - 3x)(x2 - 3x - 1) - 20.

Solution 17

(x2 - 3x)(x2 - 3x - 1) - 20

= (x2 - 3x)[(x2 - 3x) - 1] - 20

= a[a - 1] - 20 ….(Taking x2 - 3x = a)

= a2 - a - 20

= a2 - 5a + 4a - 20

= a(a - 5) + 4(a - 5)

= (a - 5)(a + 4)

= (x2 - 3x - 5)(x2 - 3x + 4)

Question 18

Find each trinomial (quadratic expression), given below, find whether it is factorisable or not. Factorise, if possible.

(i) x2 - 3x - 54

(ii) 2x2 - 7x - 15

(iii) 2x2 + 2x - 75

(iv) 3x2 + 4x - 10

(v) x(2x - 1) - 1

Solution 18

Question 19

Solution 19

Question 20

Give possible expressions for the length and the breadth of the rectangle whose area is

12x2 - 35x + 25

Solution 20

12x2 - 35x + 25

= 12x2 - 20x - 15x + 25

= 4x(3x - 5) - 5(3x - 5)

= (3x - 5)(4x - 5)

Thus,

Length = (3x - 5) and breadth = (4x - 5)

OR

Length = (4x - 5) and breadth = (3x - 5)

## Chapter 5 - Factorisation Exercise Ex. 5(C)

Question 1

Factorize :

25a2 - 9b2

Solution 1

Question 2

Factorize :

a2 - (2a + 3b)2

Solution 2

Question 3

Factorize :

a2 - 81 (b-c)2

Solution 3

Question 4

Factorize :

25(2a - b)2 - 81b2

Solution 4

Question 5

Factorize :

50a3 - 2a

Solution 5

Question 6

Factorize :

4a2b - 9b3

Solution 6

Question 7

Factorize :

3a5 - 108a3

Solution 7

Question 8

Factorize :

9(a - 2)2 - 16(a + 2)2

Solution 8

Question 9

Factorize :

a4 - 1

Solution 9

Question 10

Factorize :

a3 + 2a2 - a-2

Solution 10

Question 11

Factorize :

(a + b)3 - a - b

Solution 11

Question 12

Factorize :

a (a - 1) - b (b - 1)

Solution 12

Question 13

Factorize :

4a2 - (4b2 + 4bc + c2)

Solution 13

Question 14

Factorize :

4a2 - 49b2 + 2a - 7b

Solution 14

Question 15

Factorize :

9a2 + 3a - 8b - 64b2

Solution 15

Question 16

Factorize :

4a2 - 12a + 9 - 49b2

Solution 16

Question 17

Factorize :

4xy - x2 - 4y2 + z2

Solution 17

Question 18

Factorize :

a2 + b2 - c2 - d2 + 2ab - 2cd

Solution 18

Question 19

Factorize :

4x2 - 12ax - y2 - z2 - 2yz + 9a2

Solution 19

Question 20

Factorize :

(a2 - 1) (b2 - 1) + 4ab

Solution 20

Question 21

Factorize :

x4 + x2 + 1

Solution 21

Question 22

Factorize :

(a2 + b2 - 4c2)2 - 4a2b2

Solution 22

Question 23

Factorize :

(x2 + 4y2 - 9z2)2 - 16x2y2

Solution 23

Question 24

(a + b) 2 - a2 + b2

Solution 24

Question 25

a2 - b2 - (a + b) 2

Solution 25

Question 26

9a2 - (a2 - 4) 2

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

4x4 - x2 - 12x - 36

Solution 29

Question 30

a2 ( b + c) - (b + c)3

Solution 30

## Chapter 5 - Factorisation Exercise Ex. 5(D)

Question 1

Factorize :

a3 - 27

Solution 1

Question 2

Factorize :

1 - 8a3

Solution 2

Question 3

Factorize :

64 - a3b3

Solution 3

Question 4

Factorize :

a6 + 27b3

Solution 4

Question 5

Factorize :

3x7y - 81x4y4

Solution 5

Question 6

Factorize :

a3 -

Solution 6

Question 7

Factorize :

a3 + 0.064

Solution 7

Question 8

Factorize :

a4 - 343a

Solution 8

Question 9

Factorise:

(x - y)3 - 8x3

Solution 9

= (x - y)3 - (2x)3

= (x - y - 2x)[(x - y)2 + 2x(x - y) + (2x)2]

[Using identity (a3 - b3) = (a - b)(a2 + ab + b2)]

= (-x - y)[x2 + y2 - 2xy + 2x2 - 2xy + 4x2]

=-(x + y) [7x2 - 4xy + y2]

Question 10

Factorize :

Solution 10

Question 11

Factorize :

a6 - b6

Solution 11

Question 12

Factorize :

a6 - 7a3 - 8

Solution 12

Question 13

Factorize :

a3 - 27b3 + 2a2b - 6ab2

Solution 13

Question 14

Factorize :

8a3 - b3 - 4ax + 2bx

Solution 14

Question 15

Factorize :

a - b - a3 + b3

Solution 15

Question 16

Factorise:

2x3 + 54y3 - 4x - 12y

Solution 16

= 2(x3 + 27y3 - 2x - 6y)

= 2{[(x)3+(3y)3] - 2(x  + 3y)}

[Using identity (a3 +  b3) = (a + b)(a2 - ab + b2)]

=2{[(x + 3y)(x2 - 3xy + 9y2)] - 2(x + 3y)}

=2(x + 3y)(x2 - 3xy + 9y2 - 2)

Question 17

1029 - 3x3

Solution 17

1029 - 3x3

= 3(343 - x3)

= 3(73 - x3)

= 3(7 - x)(72 + 7x + x2)

= 3(7 - x)(49 + 7x + x2)

Question 18

Show that:

(i) 133 - 53 is divisible by 8

(ii)353 + 273 is divisible by 62

Solution 18

(i) (133 - 53)

[Using identity (a3 - b3) = (a - b)(a2 + ab + b2)]

=(13 - 5)(132 + 13 × 5 + 52)

=8(169 + 65 + 25)

Therefore, the number is divisible by 8.

(ii) (353 + 273)

[Using identity (a3 + b3)=(a + b)(a2 - ab + b2)]

=(35 + 27)(352 + 35× 27 + 272)

=62 × (352 + 35 × 27 + 272)

Therefore, the number is divisible by 62.

Question 19

Solution 19

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