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Question
Factorise the following algebraic expression by using the identity a2 – b2 = (a + b)(a – b)
x4 – y4
Solution
Let x4 – y4 = (x2)2 – (y2)2
We have a2 – b2 = (a + b)(a – b)
(x2)2 – (y2)2 = (x2 + y2)(x2 – y2)
x4 – y4 = (x2 + y2)(x2 – y2)
Again we have x2 – y2 = (x + y)(x – y)
∴ x4 – y4 = (x2 + y2)(x + y)(x – y)
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