Answer
$(\sqrt[3]{x}+1)(\sqrt[3]{x}-4\sqrt{x}+7)=\sqrt[3]{x^{2}}-4\sqrt[6]{x^{5}}+8\sqrt[3]{x}-4\sqrt{x}+7$
Work Step by Step
$(\sqrt[3]{x}+1)(\sqrt[3]{x}-4\sqrt{x}+7)$
Evaluate the product:
$\sqrt[3]{x^{2}}-4\sqrt[3]{x}\sqrt{x}+7\sqrt[3]{x}+\sqrt[3]{x}-4\sqrt{x}+7=...$
Simplify:
$...=\sqrt[3]{x^{2}}-4(x^{1/3})(x^{1/2})+8\sqrt[3]{x}-4\sqrt{x}+7=...$
$...=\sqrt[3]{x^{2}}-4x^{5/6}+8\sqrt[3]{x}-4\sqrt{x}+7=...$
$...=\sqrt[3]{x^{2}}-4\sqrt[6]{x^{5}}+8\sqrt[3]{x}-4\sqrt{x}+7$
