Answer
$x^3+4x^2y+4xy^2+y^3$
Work Step by Step
Using the Distributive Property, the product of the given expression, $
(x+y)(x^2+3xy+y^2)
,$ is
\begin{array}{l}\require{cancel}
x(x^2)+x(3xy)+x(y^2)+y(x^2)+y(3xy)+y(y^2)
\\\\=
x^3+3x^2y+xy^2+x^2y+3xy^2+y^3
\\\\=
x^3+(3x^2y+x^2y)+(xy^2+3xy^2)+y^3
\\\\=
x^3+4x^2y+4xy^2+y^3
.\end{array}
