Question

HELP PLEASE!!! I'LL GIVE BRAINELIEST AWARD TO THE PERSON WHO GIVES THE MOST DETAILED ANSWER. THANK YOU!

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

The whole shaded area is a rectangle that is:
x+10 by 2x+5

Then there is a plain white square inside the larger rectangle that is:
x+1 by x+1

Answer 1

First you need to find the area of the large rectangle then subtract the area of the smaller triangle.
area of the large triangle: (x + 10)(2x + 5), FOIL, 2x^2 + 5x + 20x + 50 =
2x^2 + 25x + 50.
area of the small rectangle: (x + 1)(x + 1), FOIL, x^2 + x + x + 1 =
x^2 + 2x + 1
Shaded region: 2x^2 + 25x + 50 -(x^2 + 2x + 1) =
x^2 + 23x + 49