A rectangular photograph is mounted on a square piece of cardboard whose sides have length x. the border that surrounds the photo is three inches on each side and 4 inches on both the top and bottom. Which of the following expressions represents the area of the photograph? Choose all that apply
x^2
(x+8)(x-6)
(x-8)(x-6)
x^2 +48
x^2 - 48
x^2 + 14x + 48
x^2 - 14x+ 48
To find the area of the photograph, we need to subtract the area of the surrounding border from the area of the cardboard.
Since the cardboard has length x and the border is 3 inches on each side, the length of the photograph will be x - 6 inches.
Similarly, since the cardboard has width x and the border is 4 inches on the top and bottom, the width of the photograph will be x - 8 inches.
Therefore, the area of the photograph is (x - 6)(x - 8).
This can be expanded to x^2 - 14x + 48.
So the correct expressions that represent the area of the photograph are:
(x - 6)(x - 8) and x^2 - 14x + 48.