Answer
$(4x^2+25y^2)(2x+5y)(2x-5y)$
Work Step by Step
Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the given $\text{
expression,
}$ $
16x^4-625y^4
,$ is equivalent to
\begin{align*}
&
(4x^2)^2-(25y^2)^2
\\&=
(4x^2+25y^2)(4x^2-25y^2)
.\end{align*}
Since the second factor above is still a difference of $2$ squares, then it can be further factored using the same method above. That is,
\begin{align*}
&
(4x^2+25y^2)[(2x)^2-(5y)^2]
\\&=
(4x^2+25y^2)[(2x+5y)(2x-5y)]
\\&=
(4x^2+25y^2)(2x+5y)(2x-5y)
.\end{align*}
Hence, the given expression simplifies to $
(4x^2+25y^2)(2x+5y)(2x-5y)
$.
