Question

Factorise: (a²-1)(b²-1)+4ab


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Answer 1

$(a2 - 1) (b2 - 1) + 4ab \\ = a2b2 - a2 - b2 + 1 + 2ab + 2ab \\ = (ab)2 + 2(ab)(1) + 12 - (a2 - 2ab + b2) \\ = (ab + 1)2 - (a - b)2 \\ = (ab + 1 + a - b)(ab + 1 - a + b)$