Question -
Answer -
(i)4p2 – 9q2
= (2p)2 – (3q)2
= (2p – 3q) (2p + 3q)
[∵ a2 – b2 = (a + b)(a – b)]
(ii) 63a2 – 112b2
= 7(9a2 – 16b2)
= 7 [(3a)2 – (4b)2]
= 7(3a – 4b)(3a + 4b)
[∵ a2 – b2 = (a + b)(a – b)]
(iii)49x2 – 36 = (7x)2 – (6)2
= (7x – 6) (7x + 6)
[∵ a2 – b2 = (a + b)(a – b)]
(iv)16x5 – 144x3 = 16x3 (x2 – 9)
= 16x3 [(x)2 – (3)2]
= 16x3(x – 3)(x + 3)
[∵ a2 – b2 = (a + b)(a – b)]
(v)(l + m)2 – (l – m)2
= (l + m) – (l – m)] [(l + m) + (l – m)]
[∵ a2 – b2 = (a + b)(a – b)]
= (l + m – l + m)(l + m + l – m)
= (2m) (2l)
= 4ml
(vi) 9x2y2 – 16 = (3xy)2 – (4)2
= (3xy – 4)(3xy + 4)
[∵ a2 – b2 = (a + b)(a – b)]
(vii)(x2 – 2xy + y2) – z2
= (x – y)2 – z2
= (x – y – z) (x – y + z)
[∵ a2 – b2 = (a + b)(a – b)]
(viii)25a2 – 4b2 + 28bc – 49c2
= 25a2 – (4b2 – 28bc + 49c2)
= (5a)2 – (2b – 7c)2
= [5a – (2b – 7c)] [5a + (2b – 7c)]
= (5a – 2b + 7c)(5a + 2b – 7c)