Factorise the following:$x^8 - y^8$

Given :

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), (x - y)$.

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Updated on: 10-Oct-2022

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