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Factorise the following polynomial:
$x^8 - y^8$
Given :
The given polynomial is $x^8 - y^8$.
To do :
We have to factorise the given polynomial.
Solution :
We know that,
$a^2 - b^2 = (a+b)(a-b)$
Therefore,
$x^8 - y^8 =(x^4)^2 - (y^4)^2$
$ = (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)$
Therefore,
The factors of the polynomial $x^8 - y^8$ are $(x^4 + y^4)(x^2 + y^2)(x+y)$ and $(x-y)$
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