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
