Answer
$28a^{3}b^{5}+8a^{2}b^{3}$
Work Step by Step
Using the Distributive Property, the product of the given expression, $
4ab^2(7a^2b^3+2ab)
,$ is
\begin{array}{l}\require{cancel}
4ab^2(7a^2b^3)+4ab^2(2ab)
\\\\=
28a^{1+2}b^{2+3}+8a^{1+1}b^{2+1}
\\\\=
28a^{3}b^{5}+8a^{2}b^{3}
.\end{array}