#### Answer

$x^4-4$

#### 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 product of the given expression, $
(x^2+2)(x^2-2)
,$ is
\begin{array}{l}\require{cancel}
(x^2)^2-(2)^2
\\\\=
x^4-4
.\end{array}