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Find the value of (x – y) (x + y) (x2 + y2).

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We know that (a – b) (a + b) = a2 – b2

Put a = x and b = y in the identity (1) then

(x – y) (x + y) = x2 – y2

Now (x – y)(x + y)(x2 + y2) = (x2 – y2) (x2 + y2)

Again put a = x2 and b = y2 in (1)

We have (x2 – y2) (x2 + y2) = (x2)2 – (y2)2 

= x4 – y4

So (x – y) (x + y) (x2 + y2) = x4 – y4

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