Final answer:
The expression for the green lawn is 15 - 8x².
Step-by-step explanation:
The area of the circular courtyard is given by the expression 15-2x². The area of each rectangular flowerbed is given by the expressions 4x² and 2x². To find the expression for the green lawn, we need to subtract the area of the flowerbeds from the area of the courtyard.
Green Lawn Area = Area of Courtyard - Area of Flowerbeds
Green Lawn Area = (15-2x²) - (4x² + 2x²)
Simplifying the expression, we get:
Green Lawn Area = 15-2x² - 4x² - 2x²
Green Lawn Area = 15 - 8x²