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

1 Answer
Mar 20, 2018

Answer:

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#