## Elementary Algebra

$(ab-1)(a^2b^2+ab+1)$
Using $a^3-b^3=(a-b)(a^2+ab+b^2)$, or the factoring of the difference of $2$ cubes, the factored form of the given expression, $a^3b^3-1 ,$ is \begin{array}{l}\require{cancel} (ab-1)[(ab)^2+ab(1)+(1)^2] \\\\= (ab-1)(a^2b^2+ab+1) .\end{array}