Answer
$4x^4-4x^2y^2+y^4$
Work Step by Step
Using $(a\pm b)^2=a^2\pm2ab+b^2$ or the square of a binomial, the square of the given expression, $
(2x^2+y^2)^2
,$ is
\begin{array}{l}\require{cancel}
(2x^2)^2-2(2x^2)(y^2)+(y^2)^2
\\\\=
4x^4-4x^2y^2+y^4
.\end{array}