Question

Help? Problem: Write an expression for the area of the shaded region in its simplest form. Show all of your steps.

Answer 1

The expression for the area of the shaded region is x² - 23x - 49

Explanation:

Area of a rectangle

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

Answer 2

Answer: x² + 23x + 49

Explanation:

The way to find the area of the shaded region is to find the area of the big rectangle, and subtract from it the area of the small square inside.

Simple enough! lets write it in algebra and work out the steps:

Area of Shaded = Area of big rectangle - Area of small square

Area of Shaded = [(x+10)(2x+5)] - [(x+1)(x+1)]

Area of Shaded = (2x² + 5x + 20x + 50) - (x² + x + x + 1)

Area of Shaded = (2x² + 25x + 50) - (x² + 2x + 1)

Area of Shaded = 2x² + 25x + 50 - x² - 2x - 1

Area of Shaded = 2x² - x² + 25x - 2x + 50 - 1

Area of Shaded = x² + 23x + 49