Answer
$40a^{3}b^{5}+22a^{2}b^{3}$
Work Step by Step
Using the Distributive Property, the product of the given expression, $
2ab^2(20a^2b^3+11ab)
,$ is
\begin{array}{l}\require{cancel}
2ab^2(20a^2b^3)+2ab^2(11ab)
\\\\=
40a^{1+2}b^{2+3}+22a^{1+1}b^{2+1}
\\\\=
40a^{3}b^{5}+22a^{2}b^{3}
.\end{array}