\(A=\left(\sqrt[3]{9}+\sqrt[3]{6}+\sqrt[3]{4}\right)\left(\sqrt[3]{3}+\sqrt[3]{2}\right)\)
\(=\left(\sqrt[3]{3}+\sqrt[3]{2}\right)\left(\sqrt[3]{3^2}+\sqrt[3]{3\cdot2}+\sqrt[3]{2^2}\right)\)
Đặt \(\sqrt[3]{3}=a;\sqrt[3]{2}=b\)
=>A=(a+b)(a^2+ab+b^2)
=a^3+a^2b+ab^2+a^2b+ab^2+b^3
=a^3+b^3+ab(a+b)
\(=3+2+\sqrt[3]{3\cdot2}\left(\sqrt[3]{3}+\sqrt[3]{2}\right)\)
\(=5+\sqrt[3]{6}\left(\sqrt[3]{3}+\sqrt[3]{2}\right)=5+\sqrt[3]{18}+\sqrt[3]{12}\)
\(\left(\sqrt[3]{9}+\sqrt[3]{6}+\sqrt[3]{4}\right)\left(\sqrt[3]{3}+\sqrt[3]{2}\right)\)
\(=\sqrt[3]{9\cdot3}+\sqrt[3]{9\cdot2}+\sqrt[3]{6\cdot3}+\sqrt[3]{6\cdot2}+\sqrt[3]{4\cdot3}+\sqrt[3]{4\cdot2}\)
\(=\sqrt[3]{27}+\sqrt[3]{18}+\sqrt[3]{18}+\sqrt[3]{12}+\sqrt[3]{12}+\sqrt[3]{8}\)
\(=3+2\sqrt[3]{18}+2\sqrt[3]{12}+2\)
\(=5+2\sqrt[3]{18}+2\sqrt[3]{12}\)
