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Factorise

(i) 16x5 − 144x3

(ii) (l + m)2 − (l − m)2

(iii) 9x2y2 − 16

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(i) 16x5 − 144x3 

= 16x3(x2 − 9)

= 16 x3 [(x)2 − (3)2]

= 16 x3(x − 3) (x + 3)  [a2 − b2 = (a − b) (a + b)]

(ii) (l + m)2 − (l − m)

= [(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

(iii) 9x2y2 − 16 = (3xy)2 − (4)2

= (3xy − 4) (3xy + 4) [a2 − b2 = (a − b) (a + b)]

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