Question:
Factorize each of the following expression:
xy9 − yx9
Solution:
$x y^{9}-y x^{9}$
$=x y\left(y^{8}-x^{8}\right)$
$=x y\left[\left(y^{4}\right)^{2}-\left(x^{4}\right)^{2}\right]$
$=x y\left(y^{4}+x^{4}\right)\left(y^{4}-x^{4}\right)$
$=x y\left(y^{4}+x^{4}\right)\left[\left(y^{2}\right)^{2}-\left(x^{2}\right)^{2}\right]$
$=x y\left(y^{4}+x^{4}\right)\left(y^{2}+x^{2}\right)\left(y^{2}-x^{2}\right)$
$=x y\left(y^{4}+x^{4}\right)\left(y^{2}+x^{2}\right)(y+x)(y-x)$
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