Question

Find an expression (where you have to multiply polynomials) to represent the shaded region of #33 and if you could also include how that would be great!

Answer 1

First, find the area of the circle using the formula A=pi r^2. 
A=pi (2x+3)^2 = pi(4x^2 + 12x + 9) 
Second, find the area of the rectangle inside by multiplying the polynomials. 
(X+1)*(3x+2) = 3x^2 + 5x +2 
Third, subtract the area of the rectangle from the area of the circle to find the area of the shaded region. 
pi(4x^2 + 12x + 9) - 3x^2 + 5x +2 =area of shaded region 
Or 
(pi (2x+3)^2) - ((X+1)(3x+2)) = area of shaded region