Answer
$(4x^2+y^2)(2x+y)(2x-y)$
Work Step by Step
Using $x^2-y^2=(x+y)(x-y)$ or the factoring of the difference of 2 squares, then the factored form of the given expression, $
16x^4-y^4
,$ is
\begin{array}{l}
(4x^2+y^2)(4x^2-y^2)
\\\\=
(4x^2+y^2)(2x+y)(2x-y)
\end{array}