Answer: x^2 + 23x + 49
Step-by-step explanation:
The area of the shaded region is the area of the big rectangle minus the square
area of rectangle
area = bh
b = 2x + 5
h = x + 10
area = (2x+5)(x+10) FOIL
= 2x^2 + 20x + 5x + 50
= 2x^2 + 25x + 50
area of square
area = s * s
s = x + 1
area = (x+1)(x+1) FOIL
= x^2 + x + x + 1
= x^2 + 2x + 1
area of shaded region
now subtract rectangle - square
(2x^2 + 25x + 50) - (x^2 + 2x + 1)
= 2x^2 + 25x + 50 - x^2 - 2x - 1 combine like terms
= x^2 + 23x + 49
