Вычислить: [tex]( \sqrt[3]{100}+2 \sqrt[3]{5}+2 \sqrt[3]{2} )( \sqrt[3]{10}- \sqrt[3]{4} )[/tex]. Created by mnyavin. algebra-ru

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Yena $(\sqrt[3]{100}+2\sqrt[3]{5}+2\sqrt[3]{2})(\sqrt[3]{10}-\sqrt[3]{4})=\\\
=\sqrt[3]{100}*(\sqrt[3]{10}-\sqrt[3]{4})+2\sqrt[3]{5}*(\sqrt[3]{10}-\sqrt[3]{4})+2\sqrt[3]{2}*(\sqrt[3]{10}-\sqrt[3]{4})=\\\
=\sqrt[3]{1000}-\sqrt[3]{400}+2\sqrt[3]{50}-2\sqrt[3]{20}+2\sqrt[3]{20}-2\sqrt[3]{8}=\\\
=10-\sqrt[3]{400}+2\sqrt[3]{50}-4=10-\sqrt[3]{400}+\sqrt[3]{400}-4=10-4=6$

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