Mathematics
(a2 - 1)(b2 - 1) + 4ab
Factorisation
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Answer
Given,
(a2 - 1)(b2 - 1) + 4ab
= a2b2 - a2 - b2 + 1 + 4ab
= a2b2 - a2 - b2 + 1 + 2ab + 2ab
= a2b2 + 2ab + 1 - a2 - b2 + 2ab
= (ab + 1)2 - (a2 + b2 - 2ab)
= (ab + 1)2 - (a - b)2
= (ab + 1 + a - b)(ab + 1 - a + b).
Hence, (a2 - 1)(b2 - 1) + 4ab = (ab + 1 + a - b)(ab + 1 - a + b).
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