Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

A rectangle is shown with length x plus 10 and width 2 x plus 5. The inside of the rectangle is shaded other than an unshaded square with length x plus 1 and width x plus 1.

Write an expression for the area of the shaded region in its simplest form. Show all of your steps.

Answer 1

x² + 23x + 49

Explanation:

area of rectangle = length × width

Area of outer rectangle:

(x + 10) × (2x + 5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50

Area of unshaded square:

(x + 1)² = x² + 2x + 1

shaded area = area of outer rectangle - area of square

shaded area = 2x² + 25x + 50 - (x² + 2x + 1) =

= 2x² + 25x + 50 - x² - 2x - 1

= x² + 23x + 49