Question

Вычислить: $( sqrt[3]{100}+2 sqrt[3]{5}+2 sqrt[3]{2} )( sqrt[3]{10}- sqrt[3]{4} )$

Answer 1

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

Answer 2

$(( sqrt[3]{10})^2+ sqrt[3]{10} * sqrt[3]{4} + (sqrt[3]{4})^2)*( sqrt[3]{10}- sqrt[3]{4} )= (sqrt[3]{10})^3- (sqrt[3]{4})^3 =10-4=6$