Distribute [tex]x[/tex]:
[tex] x^{3}+ x^{2} y+x y^{2} [/tex]
Distribute [tex]-y[/tex]
[tex] -x^{2}y-x y^{2}- y^{3} [/tex]
Combine:
[tex]x^{3}+ x^{2} y+x y^{2} + -x^{2}y-x y^{2}- y^{3}= \boxed{x^{3} - y^{3}} [/tex]
If you are familiar with special products, this is actually the pattern for the factors of the difference of two cubes.
