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15. Multiply the following expression. Assume that $$x$$ is positive.
$\left( {\sqrt[3]{x} + 2\,\,\sqrt[3]{{{x^2}}}} \right)\left( {4 - \sqrt[3]{{{x^2}}}} \right)$ Show Solution
\begin{align*}\left( {\sqrt[3]{x} + 2\,\,\sqrt[3]{{{x^2}}}} \right)\left( {4 - \sqrt[3]{{{x^2}}}} \right) & = 4\sqrt[3]{x} - \sqrt[3]{x}\,\,\sqrt[3]{{{x^2}}} + 8\,\,\sqrt[3]{{{x^2}}} - 2\,\,\sqrt[3]{{{x^2}}}\,\,\sqrt[3]{{{x^2}}}\\ & = 4\sqrt[3]{x} - \sqrt[3]{{{x^3}}} + 8\,\,\sqrt[3]{{{x^2}}} - 2\,\,\sqrt[3]{{{x^4}}}\\ & = 4\sqrt[3]{x} - \sqrt[3]{{{x^3}}} + 8\,\,\sqrt[3]{{{x^2}}} - 2\,\,\sqrt[3]{{{x^3}}}\,\,\sqrt[3]{x}\\ & = \require{bbox} \bbox[2pt,border:1px solid black]{{4\sqrt[3]{x} - x + 8\,\,\sqrt[3]{{{x^2}}} - 2x\,\,\sqrt[3]{x}}}\end{align*}