Question

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

Answer 1

See a solution process below:

Explanation:

The formula for the area of a rectangle is:

`A = l xx w`

Substituting the values from the problem gives:

`A = (2x +3)(x - 2)`

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 = (color(red)(2x) + color(red)(3))(color(blue)(x) - color(blue)(2))` becomes:

`A = (color(red)(2x) xx color(blue)(x)) - (color(red)(2x) xx color(blue)(2)) + (color(red)(3) xx color(blue)(x)) - (color(red)(3) xx color(blue)(2))`

`A = 2x^2 - 4x + 3x - 6`

We can now combine like terms:

`A = 2x^2 + (-4 + 3)x - 6`

`A = 2x^2 + (-1)x - 6`

`A = 2x^2 - 1x - 6`

`A = 2x^2 - x - 6`