Verified Answer :

JcAlmighty

The answer is x² + 23x + 49

The area of the shaded region (A) is the difference between the area of the triangle (A1) and the area of the square (A2)
A = A1 - A2

The area of the rectangle with width w and length l is:
A1 = w * l
w = 2x + 5
l = x + 10
A1 = (2x + 5)(x + 10)
Distribute it:
A1 = 2x(x + 10) + 5(x + 10)
    = 2x² + 20x + 5x + 50
    = 2x² + 25x + 50

The area of the square with side s is:
A2 = s²
s = x + 1
A2 = (x + 1)²
     = x² + 2x + 1

Thus, the area of the shaded region is
A = A1 - A2
A = 2x² + 25x + 50 - (x² + 2x + 1)
    = 2x² + 25x + 50 - x² - 2x - 1
    = 2x² - x² + 25x - 2x + 50 - 1
    = x² + 23x + 49

nobillionaireNobley

Area of the shaded region = area of the bigger rectangle - area of the smaller rectangle = (x + 10)(2x + 5) - (x + 1)^2 = (2x^2 + 25x + 50) - (x^2 + 2x + 1) = 2x^2 + 25x + 50 - x^2 - 2x - 1 = x^2 + 23x + 49

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