Question

Multiply:
$\left(\frac{3}{5}x+\frac{1}{2}y\right)\mathrm{by}\left(\frac{5}{6}x+4y\right)$

Answer 1

To multiply, we will use distributive law as follows:

$$\begin{gathered} \left(\frac{3}{5}x+\frac{1}{2}y\right)\left(\frac{5}{6}x+4y\right) \\ =\frac{3}{5}x\left(\frac{5}{6}x+4y\right)+\frac{1}{2}y\left(\frac{5}{6}x+4y\right) \\ =\frac{1}{2}{x}^2+\frac{12}{5}xy+\frac{5}{12}xy+2y^2 \\ =\frac{1}{2}{x}^2+\left(\frac{144+25}{60}\right)xy+2y^2 \\ =\frac{1}{2}{x}^2+\frac{169}{60}xy+2y^2 \end{gathered}$$

Thus, the answer is $\frac{1}{2}{x}^2+\frac{169}{60}xy+2y^2$.