Fred is given a rectangular picture frame as a birthday gift. If the length of the frame is represented by 4x-2 and the width of the frame is represented by 2x + 1, find the area of the picture frame in square inches.

Explanation:

Let L = 4x-2 be the length and W = 2x+1 be the width. The order of L and W doesn't matter.

The goal is to find the area = L*W

We could simply say L*W = (4x-2)*(2x+1) and be done. Though I have a feeling your teacher wants you to expand that out.

Let's do so

(4x-2)*(2x+1)

L(2x+1) replace "4x-2" with L

2xL + L distributive property

2x( L ) + 1( L )

2x( 4x-2 ) + 1(4x - 2) L replaced with 4x-2

2x*4x + 2x*(-2) + 1*4x + 1*(-2) distributive property twice more

8x^2 - 4x + 4x - 2

8x^2 - 2 is the final answer

Side note: you can use the FOIL rule or the box method as two alternatives to get the same answer.

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