# How do you find the product (2c-9d)^2?

Jan 21, 2017

$4 {c}^{2} - 36 c d + 81 {d}^{2}$

#### Explanation:

${\left(2 c - 9 d\right)}^{2} = 4 {c}^{2} - 36 c d + 81 {d}^{2}$

Jan 21, 2017

Use the FOIL method as you would for any other binomial. Details follow

#### Explanation:

This is the same as $\left(2 c - 9 d\right) \left(2 c - 9 d\right)$ and involves the multiplication of four products.

First: $\left(2 c\right) \cdot \left(2 c\right) = 4 {c}^{2}$

Outside: $\left(2 c\right) \cdot \left(- 9 d\right) = - 18 c d$

Inside: $\left(- 9 d\right) \cdot \left(2 c\right) = - 18 c d$

Last: $\left(- 9 d\right) \cdot \left(- 9 d\right) = 81 {d}^{2}$

Add it all up:

$4 {c}^{2} - 36 c d + 81 {d}^{2}$

Jan 21, 2017

$4 {c}^{2} - 36 c d + 81 {d}^{2}$

#### Explanation:

Given:" "(2c-9d)^2" "->" "color(blue)((2c-9d)color(red)((2c-9d))

Multiply everything in the second bracket by everything in the first

$\textcolor{red}{\textcolor{b l u e}{2 c} \left(2 c - 9 d\right) \textcolor{b l u e}{- 9 d} \left(2 c - 9 d\right)}$

$4 {c}^{2} - 18 c d - 18 c d + 81 {d}^{2}$

$4 {c}^{2} - 36 c d + 81 {d}^{2}$