# How do you find the product of (4g+3h)(2g+3h)?

May 23, 2018

$8 {g}^{2} + 18 g h + 9 {h}^{2}$

#### Explanation:

$\text{each term in the second bracket is multiplied by each}$
$\text{term in the first bracket}$

$= \left(\textcolor{red}{4 g + 3 h}\right) \left(2 g + 3 h\right)$

$= \textcolor{red}{4 g} \left(2 g + 3 h\right) \textcolor{red}{+ 3 h} \left(2 g + 3 h\right) \leftarrow \textcolor{b l u e}{\text{distribute}}$

$= \left(\textcolor{red}{4 g} \times 2 g\right) + \left(\textcolor{red}{4 g} \times 3 h\right) + \left(\textcolor{red}{3 h} \times 2 g\right) + \left(\textcolor{red}{3 h} \times 3 h\right)$

$= 8 {g}^{2} \textcolor{b l u e}{+ 12 g h} \textcolor{b l u e}{+ 6 g h} + 9 {h}^{2} \leftarrow \textcolor{m a \ge n t a}{\text{collect like terms}}$

$= 8 {g}^{2} + 18 g h + 9 {h}^{2}$