Answer
$x^2-y^4$
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, $
(x+y^2)(x-y^2)
,$ is
\begin{array}{l}\require{cancel}
(x)^2-(y^2)^2
\\\\=
x^2-y^4
.\end{array}