Answer
$5\sqrt[3]{81z^2}-3\sqrt[3]{9z}-14$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
