Solution:
1. Finding the area of the large rectangle:
- Area of large rectangle = (3x + 6)(2x + 4)
- => Area of large rectangle = 6x² + 12x + 12x + 24
- => Area of large rectangle = 6x² + 24x + 24
2. Finding the area of the small rectangle:
- Area of small rectangle = (x - 1)(x - 3)
- => Area of small rectangle = x² - 3x - x + 3
- => Area of small rectangle = x² - 4x + 3
3. Finding the area of the shaded region:
- Area of shaded region = (6x² + 24x + 24) - (x² - 4x + 3)
- => Area of shaded region = 6x² + 24x + 24 - x² + 4x - 3
- => Area of shaded region = 5x² + 28x + 21
Thus, Option D is correct.