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प्रश्न
Factorise:
(a2 - 1) (b2 - 1) + 4ab
उत्तर
(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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