Factorize:$xy^9-yx^9$


Given :

$xy^9-yx^9$

To do :

We have to factorize the given expression.

Solution :

$xy^9 – yx^9 = xy(y^8 - x^8)$

$= -xy(x^8 - y^8)$

$= -xy[(x^4)^2 - (y^4)^2]$

$= -xy (x^4 + y^4) (x^4 - y^4)$

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

$= -xy(x^4 + y^4) (x^2 + y^2) (x^2 - y^2)$

$= -xy (x^4 +y^4) (x^2 + y^2) (x + y) (x -y)$

$= -xy(x - y) (x + y) (x^2 + y^2) (x^4 + y^4)$

Hence, $xy^9 – yx^9 = -xy(x - y) (x + y) (x^2 + y^2) (x^4 + y^4)$. 

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Updated on: 10-Oct-2022

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