Enter your answer and show all the steps that you use to solve this problem in the space provided.

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

x^2 +23x +49

Step-by-step explanation:

First we find the area of the  rectangle as though the small square were not cut out of it

A = (x+10) (2x+5)

Foil

2x^2 +5x+20x+50

2x^2 +25x+50

Then we find the area of the small square

A = (x+1) (x+1)

FOIL

x^2 +x+x+1

x^2 +2x+1

Then we subtract the small square from the large rectangle to find the area of the shaded region

2x^2 +25x+50 - (x^2 +2x+1)

Distribute the minus sign

2x^2 +25x+50 - x^2 -2x-1

x^2 +23x +49