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

Question

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

1 Answer

Impact of this question

4714 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-20T10:55:58

See a solution process below:

Explanation:

The formula for the area of a rectangle is:

$A = l \times w$ $A = l xx w$

Substituting the values from the problem gives:

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

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.

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

$A = (2 x \times x) - (2 x \times 2) + (3 \times x) - (3 \times 2)$ $A = (color(red)(2x) xx color(blue)(x)) - (color(red)(2x) xx color(blue)(2)) + (color(red)(3) xx color(blue)(x)) - (color(red)(3) xx color(blue)(2))$

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

We can now combine like terms:

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

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

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

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

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question