Answer
$(a^2+25)(a+5)(a-5)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
a^4-625
,$ use the factoring of the difference of $2$ squares twice.
$\bf{\text{Solution Details:}}$
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of $2$ squares, the factored form of the expression above is
\begin{array}{l}\require{cancel}
(a^2+25)(a^2-25)
.\end{array}
The last factor is also a difference of $2$ squares. Using the factoring of the difference of $2$ squares again, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(a^2+25)(a+5)(a-5)
.\end{array}