Answer
$p^{8}-4$
Work Step by Step
Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the given expression, $
(p^4+2)(p^4-2)
$, is equivalent to
\begin{array}{l}\require{cancel}
(p^4)^2-(2)^2
\\\\=
p^{8}-4
.\end{array}