Question

Find the product:

$\left(\frac{3}{4}a+\frac{2}{3}b\right)(4a+3b)$

Answer 1

$$\begin{gathered} (\frac{3}{4}\mathrm{a}+\frac{2}{3}\mathrm{b})(4\mathrm{a}+3\mathrm{b}) \\ =\frac{3}{4}\mathrm{a}\times (4\mathrm{a}+3\mathrm{b})+\frac{2}{3}\mathrm{b}\times (4\mathrm{a}+3\mathrm{b}) \\ =(\frac{3}{4}\mathrm{a}\times 4\mathrm{a}+\frac{3}{4}\mathrm{a}\times 3\mathrm{b})+(\frac{2}{3}\mathrm{b}\times 4\mathrm{a}+\frac{2}{3}\mathrm{b}\times 3\mathrm{b}) \\ =3{\mathrm{a}}^2+\frac{9}{4}\mathrm{ab}+\frac{8}{3}\mathrm{ba}+2{\mathrm{b}}^2 \\ =3{\mathrm{a}}^2+\frac{59}{12}\mathrm{ab}+2{\mathrm{b}}^2 \end{gathered}$$