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Factorise
(i) 4p2 − 9q2
(ii) 63a2 − 112b2
(iii) 49x2 − 36
(iv) 16x5 − 144x3
(v) (l + m)2 − (l − m)2
(vi) 9x2y2 − 16
(vii) (x2 − 2xy + y2) − z2
(viii) 25a2 − 4b2 + 28bc − 49c2 Asked by Abhishek Last Modified 
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Answer
Harshit Bhardwaj
(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)
= 16 x3 [(x)2 − (3)2]
= 16 x3(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)]
[Using identity a2 − b2 = (a − b) (a + b)]
= (l + m − l + m) (l + m + l − m)
= 2m × 2l
= 4ml
= 4lm
(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 − (z)2 [(a − b)2 = a2 − 2ab + b2]
= (x − y − z) (x − y + z) [a2 − b2 = (a − b) (a + b)]
(viii) 25a2 − 4b2 + 28bc − 49c2 = 25a2 − (4b2 − 28bc + 49c2)
= (5a)2 − [(2b)2 − 2 × 2b × 7c + (7c)2]
= (5a)2 − [(2b − 7c)2]
[Using identity (a − b)2 = a2 − 2ab + b2]
= [5a + (2b − 7c)] [5a − (2b − 7c)]
[Using identity a2 − b2 = (a − b) (a + b)]
= (5a + 2b − 7c) (5a − 2b + 7c)
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