# How do you find the area of a rectangle with L = 2x + 3 and W = x - 2?

Mar 20, 2018

See a solution process below:

#### Explanation:

The formula for the area of a rectangle is:

$A = l \times w$

Substituting the values from the problem gives:

$A = \left(2 x + 3\right) \left(x - 2\right)$

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

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

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

$A = 2 {x}^{2} - 4 x + 3 x - 6$

We can now combine like terms:

$A = 2 {x}^{2} + \left(- 4 + 3\right) x - 6$

$A = 2 {x}^{2} + \left(- 1\right) x - 6$

$A = 2 {x}^{2} - 1 x - 6$

$A = 2 {x}^{2} - x - 6$