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Question
Factorise:
(a2 − 1) (b2 − 1) + 4ab
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Solution
(a2 − 1) (b2 − 1) + 4ab
= a2b2 − a2 − b2 + 1 + 4ab
= a2b2 + 1 + 2ab − a2 − b2 + 2ab
= (a2b2 + 1 + 2ab) − (a2 + b2 − 2ab)
= (ab + 1)2 − (a − b)2
= [(ab + 1) − (a − b)][(ab + 1) + (a − b)] ...[∵ a2 − b2 = (a + b)(a − b)]
= [ab + 1 − a + b][ab + 1 + a − b]
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