## Intermediate Algebra (12th Edition)

$5\sqrt[3]{81z^2}-3\sqrt[3]{9z}-14$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $(\sqrt[3]{9z}-2)(5\sqrt[3]{9z}+7) ,$ use the FOIL method and then combine like terms. $\bf{\text{Solution Details:}}$ Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{9z}(5\sqrt[3]{9z})+\sqrt[3]{9z}(7)-2(5\sqrt[3]{9z})-2(7) \\\\= 1(5)(\sqrt[3]{9z})^2+7\sqrt[3]{9z}-2(5)\sqrt[3]{9z}-14 \\\\= 5(\sqrt[3]{9z})^2+7\sqrt[3]{9z}-10\sqrt[3]{9z}-14 \\\\= 5\sqrt[3]{(9z)^2}+7\sqrt[3]{9z}-10\sqrt[3]{9z}-14 \\\\= 5\sqrt[3]{81z^2}+7\sqrt[3]{9z}-10\sqrt[3]{9z}-14 .\end{array} By combining like terms, the expression above is equivalent to \begin{array}{l}\require{cancel} 5\sqrt[3]{81z^2}+(7-10)\sqrt[3]{9z}-14 \\\\= 5\sqrt[3]{81z^2}-3\sqrt[3]{9z}-14 .\end{array}