Answer
$50x^{3}y^2-15xy^{3}$
Work Step by Step
Using the Distributive Property, the product of the given expression, $
5xy^2(10x^2-3y)
,$ is
\begin{array}{l}\require{cancel}
5xy^2(10x^2)+5xy^2(-3y)
\\\\=
50x^{1+2}y^2-15xy^{2+1}
\\\\=
50x^{3}y^2-15xy^{3}
.\end{array}