Answer
$x^4-6x^2-16$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $
(x^2+2)(x^2-8)
$, is equivalent to
\begin{array}{l}\require{cancel}
x^2(x^2)+x^2(-8)+2(x^2)+2(-8)
\\\\=
x^4-8x^2+2x^2-16
\\\\=
x^4-6x^2-16
.\end{array}
