Question

Multiply:
$\left(\frac{x}{7}+\frac{x^2}{2}\right)by\left(\frac{2}{5}+\frac{9x}{4}\right)$

Answer 1

To multiply the expressions, we will use the distributive law in the following way:

$$\begin{gathered} \left(\frac{x}{7}+\frac{x^2}{2}\right)\left(\frac{2}{5}+\frac{9x}{4}\right) \\ =\frac{x}{7}\left(\frac{2}{5}+\frac{9x}{4}\right)+\frac{x^2}{2}\left(\frac{2}{5}+\frac{9x}{4}\right) \\ =\frac{2x}{35}+\frac{9x^2}{28}+\frac{x^2}{5}+\frac{9x^3}{8} \\ =\frac{2x}{35}+\left(\frac{45+28}{140}\right)x^2+\frac{9x^3}{8} \\ =\frac{2x}{35}+\frac{73x^2}{140}+\frac{9x^2}{8} \end{gathered}$$
Thus, the answer is $\frac{2x}{35}+\frac{73x^2}{140}+\frac{9x^3}{8}$