Answer
$\color{blue}{(p^2+25)(p+5)(p-5)}$
Work Step by Step
Note that $p^4=(p^2)^2$ and $625=25^2$.
Thus, the given binomial is equivalent to:
$=(p^2)^2-25^2$
Factor the binomial using the formula $a^2-b^2=(a+b)(a-b)$ where $a=p^2$ and $b=25$ to obtain:
$=(p^2+25)(p^2-25)
\\=(p^2+25)(p^2-5^2)$
Use the same formula above to factor the second binomial with $a=p$ and $b=5$ to obtain:
$\\=\color{blue}{(p^2+25)(p+5)(p-5)}$Note that $p^4=(p^2)^2$ and $625=25^2$.
Thus, the given binomial is equivalent to:
$=(p^2)^2-25^2$
Factor the binomial using the formula $a^2-b^2=(a+b)(a-b)$ where $a=p^2$ and $b=25$ to obtain:
$=(p^2+25)(p^2-25)
\\=(p^2+25)(p^2-5^2)$
Use the same formula above to factor the second binomial with $a=p$ and $b=5$ to obtain:
$\\=\color{blue}{(p^2+25)(p+5)(p-5)}$
