Answer
$x^2y^2-a^2b^4$
Work Step by Step
Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the product of the given expression, $
(xy+ab^2)(xy-ab^2)
,$ is
\begin{array}{l}\require{cancel}
(xy)^2-(ab^2)^2
\\\\=
x^2y^2-a^2b^4
.\end{array}