Answer: 8x^2 - 2
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Step-by-step 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.