Q. 95.0( 1 Vote )

Factorize: x

Answer :

We can write x8 – y8 = (x4)2 – (y4)2


We know: a2 – b2 = (a + b)(a – b)


x8 – y8 = (x4 + y4)(x4 – y4)


Rewriting (x4 – y4) as (x2)2 – (y2)2, we have


x8 – y8 = (x4 + y4)[(x2)2 – (y2)2]


x8 – y8 = (x4 + y4)(x2 + y2)(x2 – y2)


Using the above identity to factorize (x2 – y2), we have


x8 – y8 = (x4 + y4)(x2 + y2)(x – y)(x + y)


x8 – y8 = (x – y)(x + y)(x2 + y2)(x4 + y4)


Hence, the factors of x8 – y8 are (x – y), (x + y), (x2 + y2) and (x4 + y4).


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