d) \(\left(-\dfrac{2}{3}a^3-\dfrac{3}{2}b^2\right)^3\)
\(=\left(-\dfrac{2}{3}a^3\right)^3-3\cdot\left(-\dfrac{2}{3}a^3\right)^2\cdot\dfrac{3}{2}b^2+3\cdot\left(-\dfrac{2}{3}a^3\right)\cdot\left(\dfrac{3}{2}b^2\right)^2-\left(\dfrac{3}{2}b^2\right)^3\)
\(=\dfrac{-8}{27}a^9-3\cdot\dfrac{4}{9}a^6\cdot\dfrac{3}{2}b^2+3\cdot\dfrac{-2}{3}a^3\cdot\dfrac{9}{4}b^4-\dfrac{27}{8}b^6\)
\(=\dfrac{-8}{27}a^9-2a^6b^2-\dfrac{9}{2}a^3b^4-\dfrac{27}{8}b^6\)
e) Ta có: \(\left(2m^2+\dfrac{n}{n}\right)^3\)
\(=\left(2m^2+1\right)^3\)
\(=\left(2m^2\right)^3+3\cdot\left(2m^2\right)^2+3\cdot2m^2+1\)
\(=8m^6+12m^4+6m^2+1\)
\(\left(-\dfrac{2}{3}a^2-\dfrac{3}{2}b^2\right)^3=-\dfrac{9a^6}{27}-2a^4b^2-\dfrac{9a^2b^4}{2}-\dfrac{27b^6}{8}\)
