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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Updated on: 10-Oct-2022

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