Answer
$x^3+8y^3$
Work Step by Step
Using the Distributive Property, the product of the given expression, $
(x+2y)(x^2-2xy+4y^2)
,$ is
\begin{array}{l}\require{cancel}
x(x^2)+x(-2xy)+x(4y^2)+2y(x^2)+2y(-2xy)+2y(4y^2)
\\\\=
x^3-2x^2y+4xy^2+2x^2y-4xy^2+8y^3
\\\\=
x^3+(-2x^2y+2x^2y)+(4xy^2-4xy^2)+8y^3
\\\\=
x^3+8y^3
.\end{array}
