Introductory Algebra for College Students (7th Edition)

$a^3+ab^2-a^2b-b^3$
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}