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A large rectangle has side lengths of $(x+7)$ and $(x+5)$. In the large rectangle, there is a rectangular hole with side lengths of $(2 x-3)$ and $(x-2)$. What is the area of the large rectangle (not including the area of the hole)? Express your answer as a polynomial in $x$.

 Jun 21, 2020
 #1
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We subtract the area of the bigger square from the area of the smaller square.

 

(x+7)(x+5) = x^2+12x+35

 

The larger rectangle has an expanded area of 2x^2 -7x + 6.

 

We subtract (2x^2 - 7x + 6) - (x^2+12x+35)

 

This gives us x^2 - 19x - 29

 Jun 21, 2020

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