Question

Factorise:-
x^8 - y^8​

Answer 1

The factors of $x^{8}-y^{8}$ is $(x-y)(x+y)(x^{2}+y^{2})(x^{4}+y^{4})$.

Step-by-step explanation:

The expression is:

$x^{8}-y^{8}$

Factorize the expression as follows:

$x^{8}-y^{8}=(x^{4})^{2}-(y^{4})^{2}$

            $=(x^{4}-y^{4})(x^{4}+y^{4})$

            $=[(x^{2})^{2}-(y^{2})^{2}](x^{4}+y^{4})$

            $=[(x^{2}-y^{2})(x^{2}+y^{2})](x^{4}+y^{4})$

            $=(x-y)(x+y)(x^{2}+y^{2})(x^{4}+y^{4})$

Thus, the factors of $x^{8}-y^{8}$ is $(x-y)(x+y)(x^{2}+y^{2})(x^{4}+y^{4})$.

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