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.

Guest 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) = x^{2} + 12x + 35

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

Subtracting the latter from the former comes out to –x^{2} + 15x + 49

_{.}

Guest Jan 10, 2022