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Question
Find the value of (x – y)(x + y)(x2 + y2)
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Solution
(x – y)(x + y)
Put a = x and b = y
We know that (a – b)(a + b) = a2 – b2
(x – y)(x + y) = x2 – y2
Now (x – y)(x + y)(x2 + y2)
= (x2 – y2)(x2 + y2) ........(1)
Again put a = x2 and b = y2 in (1)
(x2 – y2)(x2 + y2)
= (x2)2 – (y2)2
= x4 – y4
So (x – y)(x + y)(x2 + y2) = x4 – y4
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