The Johnsons want to cover their backyard with new grass. Their backyard is rectangular, with a length of 3x – 5 feet and a width of 4x – 10 feet. However, their rectangular swimming pool, along with its surrounding patio, has dimensions of x + 8 by x – 2 feet. What is the area of the region of the yard that they want to cover with new grass?
Assuming that all but the swimming pool is grass ....
grass area = total area - swimming pool area
= (3x-5)(4x-1) - (x+8)(x-2)
= 12x^2 - 23x + 5 - (x^2 + 6x - 16)
= 11x^2 - 29x + 21