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

Answer:

x² + 23x + 49

Step-by-step explanation:

Since the area of a rectangle is: A = l x w, where l = length and w = width, we can find the overall area of the shaded region by multiplying the entire area and subtracting the smaller area of the unshaded square:

(2x + 5)(x + 10) - (x + 1)² or (2x + 5)(x + 10) - (x² + 2x + 1)

Distribute/FOIL:  

2x² + 20x + 5x + 50 - x² - 2x -1

Combine like terms:

x² + 23x + 49