Answer
$a^3+ab^2-a^2b-b^3$
Work Step by Step
Using $(a+b)(c+d)=ab+ad+bc+bd$ or the FOIL Method, the product of the given expression, $
(a-b)(a^2+b^2)
,$ is
\begin{array}{l}\require{cancel}
a(a^2)+a(b^2)-b(a^2)-b(b^2)
\\\\=
a^3+ab^2-a^2b-b^3
.\end{array}