Question

Find the product:

$\frac{-4}{27}xyz\left(\frac{9}{2}{x}^{2}yz-\frac{3}{4}xy{z}^2\right)$

Answer 1

$$\begin{gathered} =\frac{-4}{27}\mathrm{xyz}\times \frac{9}{2}{\mathrm{x}}^2\mathrm{yz}-(\frac{-4}{27}\mathrm{xyz}\times \frac{3}{4}{\mathrm{xyz}}^2) \\ =\frac{-4}{27}\times \frac{9}{2}\times \mathrm{x}\times {\mathrm{x}}^2\times \mathrm{y}\times \mathrm{y}\times \mathrm{z}\times \mathrm{z}+\frac{4}{27}\times \frac{3}{4}\times \mathrm{x}\times \mathrm{x}\times \mathrm{y}\times \mathrm{y}\times \mathrm{z}\times {\mathrm{z}}^2 \\ =\frac{-2}{3}\times {\mathrm{x}}^{(1+2)}\times {\mathrm{y}}^{(1+1)}\times {\mathrm{z}}^{(1+1)}+\frac{1}{9}\times {\mathrm{x}}^{(1+1)}\times {\mathrm{y}}^{(1+1)}\times {\mathrm{z}}^{(1+2)} \\ =\frac{-2}{3}{\mathrm{x}}^3{\mathrm{y}}^2{\mathrm{z}}^2+\frac{1}{9}{\mathrm{x}}^2{\mathrm{y}}^2{\mathrm{z}}^3 \end{gathered}$$