SELINA Solutions for Class 9 Maths Chapter 5 - Factorisation

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

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

Question 8

Factorize by the grouping method:

ab - 2b + a2 - 2a

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Question 9

Factorize by the grouping method:

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

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 10

Factorize by the grouping method:

a2 + b - ab - a

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 11

Factorize by the grouping method:

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

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

Question 12

Factorize by the grouping method:

a2x2 + (ax2 + 1) x + a

Solution 12

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 13

Factorize by the grouping method:

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

Solution 13

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

Question 14

Factorize by the grouping method:

a (a -4) - a + 4

Solution 14

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

Question 15

Factorize by the grouping method:

y2 - (a + b) y + ab

Solution 15

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 16

Factorize by the grouping method:

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Solution 16

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

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

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 2

Factorize:

a2 - 3a - 40

Solution 2

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 3

Factorize:

1 - 2a - 3a2

Solution 3

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 4

Factorize:

x2 - 3ax - 88a2

Solution 4

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 5

Factorize:

6a2 - a-15

Solution 5

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 6

Factorize:

24a3 + 37a2 - 5a

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 7

Factorize:

a(3a - 2) - 1

Solution 7

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 8

Factorize:

a2b2 + 8ab - 9

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

Question 9

Factorize:

3 - a (4 + 7a)

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 10

Factorize:

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

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 11

Factorize:

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

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 12

Factorize:

3a2 - 1 - 2a

Solution 12

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 13

Factorize:

x2 + 3x + 2 + ax + 2a

Solution 13

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

Question 14

Factorize:

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

Solution 14

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 15

Factorize:

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

Solution 15

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

 

 

 

 

 

 

 

 

Question 16

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Solution 16

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

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

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Question 19

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Solution 19

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

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

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 2

Factorize :

a2 - (2a + 3b)2

Solution 2

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

Question 3

Factorize :

a2 - 81 (b-c)2

Solution 3

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 4

Factorize :

25(2a - b)2 - 81b2

Solution 4

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 5

Factorize :

50a3 - 2a

Solution 5

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 6

Factorize :

4a2b - 9b3

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 7

Factorize :

3a5 - 108a3

Solution 7

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 8

Factorize :

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

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

Question 9

Factorize :

a4 - 1

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 10

Factorize :

a3 + 2a2 - a-2

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 11

Factorize :

(a + b)3 - a - b

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 12

Factorize :

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

Solution 12

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 13

Factorize :

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

Solution 13

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 14

Factorize :

4a2 - 49b2 + 2a - 7b

Solution 14

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 15

Factorize :

9a2 + 3a - 8b - 64b2

Solution 15

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 16

Factorize :

4a2 - 12a + 9 - 49b2

Solution 16

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 17

Factorize :

4xy - x2 - 4y2 + z2

Solution 17

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 18

Factorize :

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

Solution 18

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 19

Factorize :

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

Solution 19

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

Question 20

Factorize :

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

Solution 20

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 21

Factorize :

x4 + x2 + 1

Solution 21

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 22

Factorize :

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

Solution 22

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

Question 23

Factorize :

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

Solution 23

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 24

(a + b) 2 - a2 + b2

Solution 24

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Question 25

a2 - b2 - (a + b) 2

Solution 25

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Question 26

9a2 - (a2 - 4) 2

Solution 26

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Question 27

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Solution 27

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation 

Question 28

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Solution 28

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation 

Question 29

4x4 - x2 - 12x - 36

Solution 29

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Question 30

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

Solution 30

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Chapter 5 - Factorisation Exercise Ex. 5(D)

Question 1

Factorize :

a3 - 27

Solution 1

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 2

Factorize :

1 - 8a3

Solution 2

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 3

Factorize :

64 - a3b3

Solution 3

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 4

Factorize :

a6 + 27b3

Solution 4

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 5

Factorize :

3x7y - 81x4y4

Solution 5

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 6

Factorize :

a3 - Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 7

Factorize :

a3 + 0.064

Solution 7

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 8

Factorize :

a4 - 343a

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

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 :

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Question 11

Factorize :

a6 - b6

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 12

Factorize :

a6 - 7a3 - 8

Solution 12

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 13

Factorize :

a3 - 27b3 + 2a2b - 6ab2

Solution 13

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 14

Factorize :

8a3 - b3 - 4ax + 2bx

Solution 14

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 15

Factorize :

a - b - a3 + b3

Solution 15

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

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

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Solution 19

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Chapter 5 - Factorisation Exercise Ex. 5(E)

Question 1

Factorize :

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

Solution 1

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

 

 

Question 2

Factorize :

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

Solution 2

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

 

 

 

 

 

Question 3

Factorize :

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Solution 3

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

Question 4

Factorize :

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Solution 4

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

Question 5

Factorize :

4x4 + 9y4 + 11x2y2

Solution 5

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

 

Question 6

Factorize :

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

Question 7

Factorize :

a - b - 4a2 + 4b2

Solution 7

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

 

 

 

Question 8

Factorize :

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

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

 

Question 9

Factorize :

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

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

Question 10

Factorize :

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

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

Question 11

Factorize :

x4 + y4 - 3x2y2

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

Question 12

Factorize :

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

Solution 12

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Question 13

Factorize :

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

Solution 13

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

 

Question 14

Factorize :

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

Solution 14

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

Question 15

Factorize :

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

Solution 15

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

 

 

 

 

Question 16

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

Solution 16

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Question 17

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Solution 17

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation 

Question 18

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Solution 18

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation 

Question 19

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

Solution 19

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Question 20

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation

Solution 20

Selina Solutions Icse Class 9 Mathematics Chapter - Factorisation