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.

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

594 square inches

step-by-step explanation:

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