Answer:
4x³ - x² - 10x + 6
Step-by-step explanation:
Area of the shaded region = area of the larger rectangle - area of the smaller rectangle
Area of the larger rectangle = L*W
L = 4x - 2
W = x² - 3
Area = (4x - 2)(x² - 3)
= 4x(x² - 3) -2(x² - 3)
= 4x³ - 12x - 2x² + 6
= 4x³ - 2x² - 12x + 6
Area of the smaller rectangle = L*W
L = x + 2
W = x
Area = (x + 2)(x)
= x² + 2x
Area of the shaded region = (4x³ - 2x² - 12x + 6) - (x² + 2x)
4x³ - 2x² - 12x + 6 - x² + 2x
Add like terms
4x³ - 2x² - x² - 12x + 2x + 6
Area of shaded region = 4x³ - x² - 10x + 6
