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Question
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
x4 – y4 + x2 – y2
Solution
We have,
x4 – y4 + x2 – y2 = (x2)2 – (y2)2 + (x2 + y2)
= (x2 + y2)(x2 – y2) + (x2 – y2)
= (x2 – y2)(x2 + y2 + 1)
= (x + y)(x – y)(x2 + y2 + 1)
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