To find the area of the shaded region, we first need to find the area of the entire rectangle and then subtract the area of the unshaded square.
Area of rectangle = length * width
= (x + 10)(2x + 5)
= 2x^2 + 5x + 20x + 50
= 2x^2 + 25x + 50
Area of unshaded square = (x + 1)(x + 1)
= x^2 + x + x + 1
= x^2 + 2x + 1
Area of shaded region = Area of rectangle - Area of unshaded square
= 2x^2 + 25x + 50 - (x^2 + 2x + 1)
= 2x^2 + 25x + 50 - x^2 - 2x - 1
= x^2 + 23x + 49
Therefore, the expression for the area of the shaded region in its simplest form is x^2 + 23x + 49.
Enter your answer and show all the steps that you use to solve this problem in the space provided.
A rectangle is shown with length x plus 10 and width 2 x plus 5. The inside of the rectangle is shaded other than an unshaded square with length x plus 1 and width x plus 1.
Write an expression for the area of the shaded region in its simplest form. Show all of your steps.
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