#### Answer

$(25+x^2)(5+x)(5-x)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To factor the given expression, $
625-x^4
,$ use the factoring of the difference of $2$ squares.
$\bf{\text{Solution Details:}}$
The expressions $
625
$ and $
x^4
$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $
625-x^4
,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(25)^2-(x^2)^2
\\\\=
(25+x^2)(25-x^2)
.\end{array}
The expressions $
25
$ and $
x^2
$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $
25-x^2
,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(25+x^2)[(5)^2-(x)^2]
\\\\=
(25+x^2)[(5+x)(5-x)]
\\\\=
(25+x^2)(5+x)(5-x)
.\end{array}