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 $x$.

Guest Jun 21, 2020

#1**+1 **

The area of the entire large rectangle is (x+7)(x+5). The hole is (2x-3)(x-2). Not including the area of the hole, the area of the large rectangle would be (x+7)(x+5)-(2x-3)(x-2).

(x+7)(x+5)-(2x-3)(x-2)

=x^2+12x+35-2x^2-7x+6

=**-x^2+19x+29**

gwenspooner85 Jun 21, 2020