Answer
$n^4-4n^3+8n-32$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $
(n^3+8)(n-4)
$, is equivalent to
\begin{array}{l}\require{cancel}
n^3(n)+n^3(-4)+8(n)+8(-4)
\\\\=
n^4-4n^3+8n-32
.\end{array}