Question

Write an expression for the area of the shaded region in its simplest form. show all of your steps

Answer 1

The answer is x² + 23x + 49

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

A1 = (x + 10)(2x + 5)
    = 2x² + 5x + 20x + 50
    = 2x² + 25x + 50
A2 = (x +1 )² = x² + 2x + 1

A = A1 - A2
    = 2x² + 25x + 50 - (x² + 2x + 1)
    = 2x² + 25x + 50 - x² - 2x - 1
    = x² + 23x + 49