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

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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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