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x^{2}\left(-x+y\right)-9\left(-x+y\right)
Do the grouping x^{2}y-x^{3}-9y+9x=\left(x^{2}y-x^{3}\right)+\left(-9y+9x\right), and factor out x^{2} in the first and -9 in the second group.
\left(-x+y\right)\left(x^{2}-9\right)
Factor out common term -x+y by using distributive property.
\left(x-3\right)\left(x+3\right)
Consider x^{2}-9. Rewrite x^{2}-9 as x^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(x-3\right)\left(x+3\right)\left(-x+y\right)
Rewrite the complete factored expression.