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Question
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
a4 – (a – b)4
Solution
We have,
a4 – (a – b)4 = (a2)2 – [(a – b)2]2
= [a2 + (a – b)2][a2 – (a – b)2]
= [a2 + a2 + b2 – 2ab][a2 – (a2 + b2 – 2ab)]
= [2a2 + b2 – 2ab][–b2 + 2ab]
= (2a2 + b2 – 2ab)(2ab – b2)
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