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Question
Factorise the following:
(a2 – b2)(c2 – d2) – 4abcd
Sum
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Solution
(a2 – b2)(c2 – d2) – 4abcd
= a2c2 – a2d2 – b2c2 + b2d2 – 4abcd
= a2c2 + b2d2 – 2abcd – a2d2 – b2c2 – 2abcd
= (a2c2 + b2d2 – 2abcd) – (a2d2 + b2c2 + 2abcd)
= (ac – bd)2 – (ad + bc)2
= [(ac – bd) + (ad + bc)][(ac – bd) – (ad + bc)]
= (ac – bd + ad + bc)(ac – bd – ad – bc).
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Method of Factorisation : Difference of Two Squares
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