x y^9-y x^9 =x y (y^8-x^8 ) =x y [ (y^4 )^2- (x^4 )^2 ] =x y (y^4+x^4 ) [ (y^2 )^2- (x^2 )^2 ] =x y (y^4+x^4 ) (y^2+x^2 ) (y^2-x^2 ) =x y (y^4+x^4 ) (y^2+x^2 )(y+x)(y-x)

Solve: x y^9-y x^9

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Question

Solve:
$x y^9-y x^9$

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Answer

$x y^9-y x^9$
$=x y\left(y^8-x^8\right)$
$=x y\left[\left(y^4\right)^2-\left(x^4\right)^2\right]$
$=x y\left(y^4+x^4\right)\left[\left(y^2\right)^2-\left(x^2\right)^2\right]$
$=x y\left(y^4+x^4\right)\left(y^2+x^2\right)\left(y^2-x^2\right)$
$=x y\left(y^4+x^4\right)\left(y^2+x^2\right)(y+x)(y-x)$

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