# SELINA Solutions for Class 9 Maths Chapter 5 - Factorisation

Page / Exercise

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

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

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]

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]

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]

Solution 5

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

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

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)

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

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

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

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

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

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)

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)

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)

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

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)

Solution 18

Solution 19

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)

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Solution 25

Solution 26

Solution 27

Solution 28

Solution 29

Solution 30

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

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

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]

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

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)

Solution 17

1029 - 3x3

= 3(343 - x3)

= 3(73 - x3)

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

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

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.

Solution 19

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

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

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