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Distribute x:
 x^{3}+ x^{2} y+x y^{2}
Distribute -y
 -x^{2}y-x y^{2}- y^{3}

x^{3}+ x^{2} y+x y^{2} +  -x^{2}y-x y^{2}- y^{3}= \boxed{x^{3} - y^{3}}

If you are familiar with special products, this is actually the pattern for the factors of the difference of two cubes.