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

The area of the shaded region will be the area of the rectangle minus the area of the white square inside of it:

((x+10)(2x+5)) - ((x+1)(x+1))

First, FOIL both of the areas separately:

(2x^2 + 5x + 20x + 50) - (x^2 + x + x + 1)

Simplify within the parentheses by adding like terms:

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

Now, subtract one equation from the other:

2x^2 + 25x + 50
-x^2  -    2x  -   1
= x^2 + 23x + 49

This will be the equation for the area.

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