Answer:
Area of grassy space is x² - 13x + 23
Step-by-step explanation:
The area of the grassy space is equal to the difference between the area of the entire yard and the area of the pool
∵ The area of the entire yard = 3x² - 14x - 5
∵ The area of the pool = (x - 4)(2x + 7)
- Lets simplify the area of the pool by multiplying the brackets
∵ (x - 4)(2x + 7) = (x)(2x) + (x)(7) + -4(2x) + -4(7)
∴ (x - 4)(2x + 7) = 2x² + 7x + (-8x) + (-28)
- Add the like terms in the right hand side
∴ (x - 4)(2x + 7) = 2x² - x - 28
Now lets find the difference between the area of the entire yard and the area of the pool to find the area of the grassy space
∵ Area of grassy space = (3x² - 14x - 5) - (2x² - x - 28)
- Multiply all the terms of the second bracket by (-)
∴ Area of grassy space = 3x² - 14x - 5 - 2x² + x + 28
- Add the like terms
∴ Area of grassy space = (3x² - 2x²) + (-14x + x) + (-5 + 28)
∴ Area of grassy space = x² + (-13x) + 23
∴ Area of grassy space = x² - 13x + 23
