Question

Find the product:

$\left(\frac{2}{5}x-\frac{1}{2}y\right)(10x-8y)$

Answer 1

$$\begin{gathered} (\frac{2}{5}\mathrm{x}-\frac{1}{2}\mathrm{y})(10\mathrm{x}-8\mathrm{y}) \\ =\frac{2}{5}\mathrm{x}\times (10\mathrm{x}-8\mathrm{y})-\frac{1}{2}\mathrm{y}\times (10\mathrm{x}-8\mathrm{y}) \\ =(\frac{2}{5}\mathrm{x}\times 10\mathrm{x}-\frac{2}{5}\mathrm{x}\times 8\mathrm{y})-(\frac{1}{2}\mathrm{y}\times 10\mathrm{x}-\frac{1}{2}\mathrm{y}\times 8\mathrm{y}) \\ =4{\mathrm{x}}^2-\frac{16}{5}\mathrm{xy}-5\mathrm{yx}+4{\mathrm{y}}^2 \\ =4{\mathrm{x}}^2-\frac{41}{5}\mathrm{xy}+4{\mathrm{y}}^2 \end{gathered}$$