First, you have to recognize that the shaded portion of the prism is a rectangle.
To find the area of a rectangle, multiply the length times the width.
In this case, the length of the rectangle is (x + 1) and the width is (x – 1).
Therefore, the area of the shaded face of the prism is
l x w
(x+1)(x-1)
FOIL to simplify the expression.
FOIL = First Outer Inner Last
First x * x = x2
Outer x * – 1 = –x
Inner 1 * x = x
Last 1 * – 1 = –1
Put it all together
x2 – x + x – 1
The –x and +x will cancel out, leaving you with
x2 – 1
Therefore, the simplified expression for the area of the shaded face of the prism is x2 – 1.
