(1) Solution:- x2+x y +z x +y z
= x( x +y) + z (x +y)
= (x +y) (x +z)
(2) Solution:- a2+bc+ ca+ a b
= a2+ a b +ca +b c
= a (a +b) + c(a +b)
= (a +b) (a + c)
(3) Solution:- a b(p x+ q y)+a2q x +b2x + b2 p y
= a b p x + a b q y + a2 q x+ b2 p y
= a b p x+ a2 q x+ b2 p y + a b q y
= a x (b p +a q) +by (b p +a q)
= (b p +a q) (a x +by)
(4) Solution:- 4x2-y2
= (2x)2 – (y)2
= (2x+y) (2x-y)
(5) Solution:- 9a2 – 4b2
= (3b)2 – (2b)2
= (3a + 2b) (3a-2b)
(6) Solution:- a2 b2 – 49y2
= (a b)2 – (7y)2
= (ab+7y) (ab-7y)
(7) Solution:- 16x4 – 81y4
= (4x2)2 – (9y2)2
= (4x2+9y2) (4x2-9y2)
= (4x2+9y2) {(2x)2 – (3y)2}
= (4x2+9y2) (2x+3y) (2x- 3y)
(8) Solution:- a2 – (x +y)2
= (a+ x+ y) (a-x-y)
(9) Solution:- (2x-3y+5z)2 – (x-2y+3z)2
= (2x-3y+5z+x-2y+3z) (2x-3y+5z-x+2y-3z)
= (3x-5y+8z) (x-y+2z)
(10) Solution:- (4a+ 8a2+9a4)
= (2)2+2x 2x 3a2+ (3a2)2 – 4a2
= (2+3a2)2 – (2a)2
= (2+ 3a2+2a) (2+ 3a2-2a)
(11) Solution:- 2a2+6a-80
= 2 (a2+3a-40)
= 2 (a2+8a-5a-40)
= 2{a (a+8) – 5 (a+8)}
= 2 (a+8) (a-5)
(12) Solution:- y2-6y- 91
= y2 – 13y+7y- 91
= y(y-13) + 7(y-13)
= (y-13) (y+7)
(13) Solution:- p2– 15p+ 56
= p2– 8p-7p+56
= p (p-8) -7(p-8)
= (p-8) (p-7)
(14) Solution:- 45a8 – 5a4x4
= 5a4 (9a4-x4)
= 5a4 {(3a2)2 – (x2)2}
= 5a4 (3a2+x2) (3a2-x2)
(15) Solution:- a2+3a-40
= a2+8a-5a-40
= a (a+8) -5 (a+8)
= (a+8) (a-5)
(16) Solution:– (x2+1)2 – (y2+1)2
= {(x2+1) + (y2+1) }{(x2+1) – (y2+1)}
= (x2+1+y2+1) (x2+1-y2-1)
= (x2+y2+2) (x +y) (x-y)
= (x2+y2+2) (x +y) (x-y)
(17) Solution:- x2+11x+30
= x2+5x+6x+30
= x (x+5) + 6 (x+5)
= (x+5) (x+6)
(18) Solution:- a2-b2+2bc-c2
= a2-(b2-2bc+c2)
= (a)2 – (b-c)2
= (a+ b-c) (a-b +c)
(19) Solution:- 144x7– 25x3 a4
= x3 (144x4– 25a4)
= x3{(12x2)2 – (5a2)2}
= x3 (12x2+5a2) (12x2-5a2)
(20) Solution:- 4x2+12xy+9y2-16a2
= (2x)2 + 2X 2 x X 3y+ (3y)2 – 16a2
= (2x+3y)2 – (4a)2
= (2x+3y+4a) (2x+3y-4a)
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