Problem

$(\sqrt[3]{x+6}-2)\left(\sqrt[3]{(x+6)^{2}}-2 \sqrt[3]{x+6}+4\right.$

Answer

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Answer

Final Answer: \(\boxed{(-2\sqrt[3]{x+6}+\sqrt[3]{(x+6)^{2}}+4)(\sqrt[3]{x+6}-2)}\)

Steps

Step 1 ：Given expression: $(\sqrt[3]{x+6}-2)\left(\sqrt[3]{(x+6)^{2}}-2 \sqrt[3]{x+6}+4\right)$

Step 2 ：Expand the expression: $(\sqrt[3]{x+6}-2)(-2\sqrt[3]{x+6}+\sqrt[3]{(x+6)^{2}}+4)$

Step 3 ：Final Answer: \(\boxed{(-2\sqrt[3]{x+6}+\sqrt[3]{(x+6)^{2}}+4)(\sqrt[3]{x+6}-2)}\)

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