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}