# How do you multiply (3b-3c)^2?

Feb 14, 2017

See the entire solution process below:

#### Explanation:

This expression can be rewritten as:

$\left(3 b - 3 c\right) \left(3 b - 3 c\right)$

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

$\left(\textcolor{red}{3 b} - \textcolor{red}{3 c}\right) \left(\textcolor{b l u e}{3 b} - \textcolor{b l u e}{3 c}\right)$ becomes:

$\left(\textcolor{red}{3 b} \times \textcolor{b l u e}{3 b}\right) - \left(\textcolor{red}{3 b} \times \textcolor{b l u e}{3 c}\right) - \left(\textcolor{red}{3 c} \times \textcolor{b l u e}{3 b}\right) + \left(\textcolor{red}{3 c} \times \textcolor{b l u e}{3 c}\right)$

$9 {b}^{2} - 9 b c - 9 b c + 9 {c}^{2}$

We can now combine like terms:

$9 {b}^{2} + \left(- 9 - 9\right) b c + 9 {c}^{2}$

$9 {b}^{2} + \left(- 18\right) b c + 9 {c}^{2}$

$9 {b}^{2} - 18 b c + 9 {c}^{2}$