Find the value

$=x y\left(y^{8}-x^{8}\right)$

$=x y\left(\left(y^{4}\right)^{2}-\left(x^{4}\right)^{2}\right)$

Using the identity $p^{2}-q^{2}=(p+q)(p-q)$

$=x y\left(y^{4}+x^{4}\right)\left(y^{4}-x^{4}\right)$

$=x y\left(y^{4}+x^{4}\right)\left(\left(y^{2}\right)^{2}-\left(x^{2}\right)^{2}\right)$

Using the identity $p^{2}-q^{2}=(p+q)(p-q)$

$=x y\left(y^{4}+x^{4}\right)\left(y^{2}+x^{2}\right)\left(y^{2}-x^{2}\right)$

$=x y\left(y^{4}+x^{4}\right)\left(y^{2}+x^{2}\right)(y+x)(y-x)$

$=x y\left(x^{4}+y^{4}\right)\left(x^{2}+y^{2}\right)(x+y)(-1)(x-y)$

$\therefore(y-x)=-1(x-y)$

$=-x y\left(x^{4}+y^{4}\right)\left(x^{2}+y^{2}\right)(x+y)(x-y)$

$\therefore x y^{9}-y x^{9}=-x y\left(x^{4}+y^{4}\right)\left(x^{2}+y^{2}\right)(x+y)(x-y)$