Answer: A = x^2 + 11x + 24
Step-by-step explanation: The area of the shaded region is the area of the rectangle - area of square, A
Therefore A = (2x + 7)(x + 4) - (x + 2)(x + 2)
A = 2x^2 + 8x + 7x + 28 - ( x^2 + 2x + 2x + 4 )
A = 2x^2 + 8x + 7x + 28 - ( x^2 + 4x + 4 )
A = 2x^2 + 15x + 28 - x^2 - 4x - 4
A = 2x^2 - x^2 + 15x - 4x + 28 - 4
A = x^2 + 11x + 24