Answer: the area of the shaded region is 5x² + 28x + 23
Step-by-step explanation:
The formula for determining the area of the rectangle is expressed as
Area = length × width
The area of the smaller rectangle is
(x - 3)(x - 1)
We would apply the distributive property by multiplying each term in one bracket by each term in the other bracket. It becomes
x² - x - 3x + 1
x² - 4x + 1
The area of the bigger rectangle is
(3x + 6)(2x + 4)
6x² + 12x + 12x + 24
6x² + 24x + 24
The area of the shaded region would be
6x² + 24x + 24 - (x² - 4x + 1)
6x² + 24x + 24 - x² + 4x - 1
6x² - x² + 24x + 4x + 24 - 1
5x² + 28x + 23