Question

Write a polynomial that represents the area of the shaded region

Answer 1

Answer: x^2-3x+36

=========================================

Explanation:

The larger rectangle has area of (x+1)(x+1) = x^2+2x+1 through the use of the FOIL rule or distribution

If you use distribution, then it might help to let y = x+1 so we'd have y(x+1) lead to xy+1y which becomes x(x+1)+1(x+1). From there it might be easier to see how to get x^2+2x+1 after everything distributes again and simplifies.

The smaller rectangle has area 5x-35 which is found by distributing 5(x-7)

To get the shaded area, we subtract the two rectangle areas found above

shaded area = (larger area) - (smaller area)

shaded area = (x^2+2x+1) - (5x - 35)

shaded area = x^2+2x+1 - 5x + 35

shaded area = x^2-3x+36