Question

Thực hiện phép tính sau:

Answer 1

\(\left(\sqrt[3]{4}+1\right)^3-\left(\sqrt[3]{4}-1\right)^3\)

\(=\left(\sqrt[3]{4}+1-\sqrt[3]{4}+1\right)\left[\left(\sqrt[3]{4}+1\right)^2+\left(\sqrt[3]{4}+1\right)\left(\sqrt[3]{4}-1\right)+\left(\sqrt[3]{4}-1\right)^2\right]\)

\(=2\left[\left(\sqrt[3]{4}\right)^2+2.\sqrt[3]{4}+1+\left(\sqrt[3]{4}\right)^2-1+\left(\sqrt[3]{4}\right)^2-2.\sqrt[3]{4}+1\right]\)

\(=2\left[3\left(\sqrt[3]{4}\right)^2+1\right]\)

\(=6.\sqrt[3]{16}+2\)