Question

Find a simplified expression for the area of the shaded region below

Answer 1

Area of the shaded region = (8x + 6)

Explanation:

Area of the shaded region = Area of the large rectangle - Area of the smaller rectangle

Area of the large rectangle = Length × width

= (x + 3)(x + 2)

= x(x + 2) + 3(x + 2)

= x² + 2x + 3x + 6

= x² + 5x + 6

Area of the smaller rectangle = x(x - 3)

= (x² - 3x)

Area of the shaded region = (x² + 5x + 6) - (x² - 3x)

= x² + 5x + 6 - x² + 3x

= (8x + 6)