Tính giá trị biểu thức \(B=(\sqrt[3]{9}-\sqrt[3]{6}+\sqrt[3]{4})(\sqrt[3]{3}+\sqrt[3]{2})\)

* Hướng dẫn giải

Ta có

\(\begin{aligned} \mathbf{B} &=(\sqrt[3]{\mathbf{9}}-\sqrt[3]{6}+\sqrt[3]{4})(\sqrt[3]{3}+\sqrt[3]{2}) \\ &=\sqrt[3]{9}(\sqrt[3]{3}+\sqrt[3]{2})-\sqrt[3]{6}(\sqrt[3]{3}+\sqrt[3]{2})+\sqrt[3]{4}(\sqrt[3]{3}+\sqrt[3]{2}) \\ &=\sqrt[3]{9} \sqrt[3]{3}+\sqrt[3]{9} \sqrt[3]{2}-\sqrt[3]{6} \sqrt[3]{3}-\sqrt[3]{6} \sqrt[3]{2}+\sqrt[3]{4} \sqrt[3]{3}+\sqrt[3]{4} \sqrt[3]{2} \\ &=\sqrt[3]{27}+\sqrt[3]{18}-\sqrt[3]{18}-\sqrt[3]{12}+\sqrt[3]{12}+\sqrt[3]{8} \\ &=\sqrt[3]{27}+\sqrt[3]{8} \\ &=3+2 \\ &=5 \end{aligned}\)