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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 2x - 7 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.

 Jan 10, 2022
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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 2x - 7 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.

 

Subtract the area of the hole from the area of the large rectangle.  

 

The area of the large rectangle is   (x + 7) • (x + 5)    =   x2 + 12x + 35  

The area of the small rectangle is   (2x – 7) • (x + 2)  =  2x2 – 3x – 14  

 

Subtracting the latter from the former comes out to      –x2 + 15x + 49  

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 Jan 10, 2022

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