jmc

Question

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-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.

Accepted Answer

The area of the large rectangle is (x+7)(x+5), and the area of the hole is (2x-3)(x-2). To get our answer, we subtract the area of the hole from the area of the large rectangle. align* (x&+7)(x+5)-(2x-3)(x-2) &=x(x+5)+7(x+5)-2x(x-2)+3(x-2) &=x^2+5x+7x+35-2x^2+4x+3x-6 &=-x^2+19x+29. align*