Introductory Algebra for College Students (7th Edition)

$$x^3 + y^3$$
We simplify this expression by using distributive property to multiply each of the terms in the binomial with each of the terms in the trinomial: $$(x)(x^2) + (x)(-xy) + (x)(y^2) + (y)(x^2) + (y)(-xy) + (y)(y^2)$$ We multiply the terms: $$x^3 - x^2y + xy^2 + x^2y - xy^2 + y^3$$ Group like terms: $$x^3 + (- x^2y + x^2y) + (xy^2 - x^2y) + y^3$$ Combine like terms to simplify: $$x^3 + y^3$$