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

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Answer 1 · 2018-03-20T10:55:58

See a solution process below:

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:

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

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

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

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