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Class 9 SELINA Solutions Maths Chapter 5 - Factorisation

Factorisation Exercise Ex. 5(A)

Solution 1(a)

Correct option: (i)

Solution 1(b)

Correct option: (iii)

Solution 1(c)

Correct option: (iii)

Solution 1(d)

Correct option: (iv)

Solution 1(e)

Correct option: (ii)

Solution 2

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

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 3

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 4

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 5

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

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

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

Solution 6

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

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

Solution 7

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 8

 

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Factorisation Exercise Ex. 5(B)

Solution 1(a)

Correct option: (iii)

Solution 1(b)

Correct option: (iv)

Solution 1(c)

Correct option: (ii)

Solution 1(d)

Correct option: (i)

Solution 1(e)

Correct option: (iii)

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

 

 

 

 

 

 

 

 

Factorisation Exercise Ex. 5(C)

Solution 1(a)

Correct option: (ii)

Solution 1(b)

Correct option: (i)   

Solution 1(c)

Correct option: (iv)

Solution 1(d)

Correct option: (i)

Solution 1(e)

Correct option: (i)

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

Factorisation Exercise Ex. 5(D)

Solution 1(a)

Correct option: (ii)   

Solution 1(b)

Correct option: (iii)   

Solution 1(c)

Correct option: (i)   

Solution 1(d)

Correct option: (iii)   

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

(x - y)3 - 8x3

= (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 11

fraction numerator 8 straight a cubed over denominator 27 end fraction minus straight b cubed over 8 equals open parentheses fraction numerator 2 straight a over denominator 3 end fraction close parentheses cubed minus open parentheses straight b over 2 close parentheses cubed
space space space space space space space space space space space space space space space space space space space space space equals open parentheses fraction numerator 2 straight a over denominator 3 end fraction minus straight b over 2 close parentheses open square brackets open parentheses fraction numerator 2 straight a over denominator 3 end fraction close parentheses squared plus fraction numerator 2 straight a over denominator 3 end fraction cross times straight b over 2 plus open parentheses straight b over 2 close parentheses squared close square brackets
left square bracket because straight a cubed space minus space straight b cubed equals left parenthesis straight a minus straight b right parenthesis left parenthesis straight a squared equals ab plus straight b squared right parenthesis right square bracket
space space space space space space space space space space space space space space space space space space space space space equals open parentheses fraction numerator 2 straight a over denominator 3 end fraction minus straight b over 2 close parentheses open square brackets fraction numerator 4 straight a squared over denominator 9 end fraction plus ab over 3 plus straight b squared over 4 close square brackets

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Factorisation Exercise Ex. 5(E)

Solution 1(a)

Correct option: (ii)

Solution 1(b)

Correct option: (iv)

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

 

Factorisation Exercise Test Yourself

Solution 1

Solution 2

x2 + y2 + x + y + 2xy

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

=(x + y)2 + (x + y) 

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

Solution 3

a2 + 4b2 - 3a + 6b - 4ab

= 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 4

m (x - 3y)2 + n (3y - x) + 5x - 15y

= 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 5

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

= (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)

Solution 6

Solution 7

(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 8

Solution 9

Solution 10

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 11

Solution 12

  

Solution 13

  

Solution 14

Solution 15

Solution 16

2x3 + 54y3 - 4x - 12y

= 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

Solution 20

Solution 21

  

Solution 22

  

Solution 23

Solution 24

  

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