# How do you multiply (2x+3v)^2?

Feb 11, 2017

See the entire solution process below.

#### Explanation:

We can rewrite this express as:

$\left(2 x + 3 v\right) \left(2 x + 3 v\right)$

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{2 x} + \textcolor{red}{3 v}\right) \left(\textcolor{b l u e}{2 x} + \textcolor{b l u e}{3 v}\right)$ becomes:

$\left(\textcolor{red}{2 x} \times \textcolor{b l u e}{2 x}\right) + \left(\textcolor{red}{2 x} \times \textcolor{b l u e}{3 v}\right) + \left(\textcolor{red}{3 v} \times \textcolor{b l u e}{2 x}\right) + \left(\textcolor{red}{3 v} \times \textcolor{b l u e}{3 v}\right)$

$4 {x}^{2} + 6 x v + 6 x v + 9 {v}^{2}$

We can now combine like terms:

$4 {x}^{2} + \left(6 + 6\right) x v + 9 {v}^{2}$

$4 {x}^{2} + 12 x v + 9 {v}^{2}$