Answer:
Step-by-step explanation:
The formula for determining the area of a rectangle is expressed as
Area = length × width
Their backyard is rectangular, with a length of 3x – 5 feet and a width of 4x – 10 feet. This means that the area of the backyard is
(3x - 5)(4x - 10)
= 12x² - 30x - 20x + 15
= (12x² - 50x + 15) square feet
Their rectangular swimming pool, along with its surrounding patio, has dimensions of x + 8 by x – 2 feet. This means that the area occupied by the swimming pool and its surrounding patio is
(x + 8)(x - 2)
= x² - 2x + 8x - 16
= x² + 6x - 16
Assuming the swimming pool and its surrounding patio will not be covered with new grass, then the area of the region of the yard that they want to cover with new grass is
12x² - 50x + 15 - (x² + 6x - 16)
= 12x² - 50x + 15 - x² - 6x + 16
= 12x² - x² - 50x - 6x + 15 + 16
= 11x² - 56x + 31 square feet
