# How do you multiply (x-4y)^2?

Jan 16, 2017

See entire solution process below:

#### Explanation:

First, we convert this expression to:

${\left(x - 4 y\right)}^{2} = \left(x - 4 y\right) \left(x - 4 y\right)$

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

$\left(\textcolor{red}{x} - \textcolor{red}{4 y}\right) \left(\textcolor{b l u e}{x} - \textcolor{b l u e}{4 y}\right)$ becomes:

$\left(\textcolor{red}{x} \times \textcolor{b l u e}{x}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{4 y}\right) - \left(\textcolor{red}{4 y} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{4 y} \times \textcolor{b l u e}{4 y}\right)$

${x}^{2} - 4 x y - 4 x y + 16 {y}^{2}$

We can now combine like terms:

${x}^{2} + \left(- 4 - 4\right) x y + 16 {y}^{2}$

${x}^{2} - 8 x y + 16 {y}^{2}$