Question

Find the product:

$\frac{2}{3}abc(a^2+b^2-3c^2)$

Answer 1

$$\begin{gathered} =\frac{2}{3}\mathrm{abc}\times {\mathrm{a}}^2+\frac{2}{3}\mathrm{abc}\times {\mathrm{b}}^2-\frac{2}{3}\mathrm{abc}\times 3{\mathrm{c}}^2 \\ =\frac{2}{3}\mathrm{a}\times {\mathrm{a}}^2\times \mathrm{b}\times \mathrm{c}+\frac{2}{3}\mathrm{a}\times \mathrm{b}\times {\mathrm{b}}^2\times \mathrm{c}-\frac{2}{3}\times 3\times \mathrm{a}\times \mathrm{b}\times \mathrm{c}\times {\mathrm{c}}^2 \\ =\frac{2}{3}\times {\mathrm{a}}^{(1+2)}\times \mathrm{b}\times \mathrm{c}+\frac{2}{3}\times \mathrm{a}\times {\mathrm{b}}^{(1+2)}\times \mathrm{c}-2\times \mathrm{a}\times \mathrm{b}\times {\mathrm{c}}^{(1+2)} \\ =\frac{2}{3}{\mathrm{a}}^3\mathrm{bc}+\frac{2}{3}{\mathrm{ab}}^3\mathrm{c}-2{\mathrm{abc}}^3 \end{gathered}$$