Question

Find the area of the shaded region

Answer 1

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