# Find the following products and express answers in simplest radical form. All va

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers.
$3\sqrt[3]{4}\left(2\sqrt[3]{2}-6\sqrt[3]{4}\right)$

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Given expression:
$3\sqrt[3]{4}\left(2\sqrt[3]{2}-6\sqrt[3]{4}\right)$
$3\sqrt[3]{4}\left(2\sqrt[3]{2}-6\sqrt[3]{4}\right)=3\sqrt[3]{4}\left(2\sqrt[3]{2}-3\sqrt[3]{4}\right)\left(6\sqrt[3]{4}\right)$
$6\sqrt[3]{4}\sqrt[3]{2}-18\sqrt[3]{4}\sqrt[3]{4}$
$=6\sqrt[3]{4×2}-18\sqrt[3]{4×4}$
$6\sqrt[3]{8}-18\sqrt[3]{16}$
$=6{\left(8\right)}^{\frac{1}{3}}-18{\left(16\right)}^{\frac{1}{3}}$
$6{\left(2×2×2\right)}^{\frac{1}{3}}-18{\left(2×2×2\right)}^{\frac{1}{3}}$
$=6\left(2\right)-18\left(2\right){\left(2\right)}^{\frac{1}{3}}$
$=12-36{\left(2\right)}^{\frac{1}{3}}$
$=12-36{\left(2\right)}^{\frac{1}{3}}$
$=12-36\sqrt[3]{2}$
Hence
$3\sqrt[3]{4}\left(2\sqrt[3]{2}-6\sqrt[3]{4}\right)=12-36\sqrt[3]{2}$