Identify the polynomial that represents the shaded area of the figure.

18m − 81
18m − 17
18m − 145
18m − 64

The area of the biggest square is x * x = x²

The area of the square on the upper right is 3*3 = 9

There are 2 rectangles, one on top of the shaded square and the other is to the right of the shaded square. Their area is 3*(x-3). Since there are two rectangles, the sum of their area is 2*3*(x-3) = 6(x-3)

Do you see how I got the length of the rectangle = x-3? I took off 3 unit from the x length for the largest square.

What they are trying to do is to have you figure out that the area of the shaded square which has a side of length x-3 is the same as the area of the larger square - area of small square - area of the two rectangles.

The area of the larger square = x²
The area of the two rectangles = 6(x-3) = 6x - 18
The area of the small square = 9

If you subtract the rectangles and small square from the larger square you have

x² - 6x + 18 - 9 ---> x² - 6x + 9

The area of the shaded square is (x-3)² = x² - 6x + 9

And that is the same as the area above.

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