Question

Write an expression for the area of the shaded region in its simplest form.

Answer 1

Answer:

area = Iw

Explanation:

area = lw

where

l = length

w = width

Therefore,

The area of the shaded region  = area of the big rectangle - area of the small rectangle

Therefore,

area of the big rectangle = (x+10)(2x+5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50

area of the small rectangle = (x+1)(x+1) = x² + x + x + 1 = x² + 2x + 1

area of the shaded region = 2x² + 25x + 50 - ( x² + 2x + 1)

area of the shaded region =  2x² + 25x + 50 - x² - 2x - 1

area of the shaded region = x² - 23x - 49