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
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
