Question

Factorize the following below given :-
X^8-y^8

Answer 1

$x^{8} - y^{8}$
⇒$(x^{4})^{2} - (y^{4})^{2}$
⇒$(x^{4} + y^{4} )(x^{4}-y^{4})$
⇒$( x^{4} +y^{4})[(x^{2})^{2}-y ^{2})^{2}]$
=$( x^{4} +y^{4})( x^{2} + y^{2} )( x^{2}- y^{2} )$
=$(x^{4} +y^{4})( x^{2} + y^{2} )( x+y)(x-y)$
Ans:$(x^{4} +y^{4})( x^{2} + y^{2} )( x+y)(x-y)$
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