Find the product of (3x + 7)(2x – 5).
Jack painted a rectangular face of a prism as shown in the figure below.
What is the simplified expression for the area of the shaded face of the prism?
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
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.
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