# How do you find the product (g+5h)^2?

Jan 16, 2017

See the full solution process below:

#### Explanation:

First, we transform this expression to:

${\left(g + 5 h\right)}^{2} = \left(g + 5 h\right) \left(g + 5 h\right)$

Now, to multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{g} + \textcolor{red}{5 h}\right) \left(\textcolor{b l u e}{g} + \textcolor{b l u e}{5 h}\right)$ becomes:

$\left(\textcolor{red}{g} \times \textcolor{b l u e}{g}\right) + \left(\textcolor{red}{g} \times \textcolor{b l u e}{5 h}\right) + \left(\textcolor{red}{5 h} \times \textcolor{b l u e}{g}\right) + \left(\textcolor{red}{5 h} \times \textcolor{b l u e}{5 h}\right)$

${g}^{2} + 5 g h + 5 g h + 25 {h}^{2}$

We can now combine like terms:

${g}^{2} + \left(5 + 5\right) g h + 25 {h}^{2}$

${g}^{2} + 10 g h + 25 {h}^{2}$