Question

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 a dimension 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?
A. x^2 + 6x - 16 ft^2

B. 6x^2 - 55x + 104 ft^2

C. 12x^2 - 50x + 50 ft^2

D. 11x^2 - 56x + 66 ft^2

Answer 1

To fond the area need to be grassed, find the area of the yard and subtract the area of the pool/patio.
(3x - 5)(4x - 10) =
12x^2 - 30x - 20x + 50 = 12x^2 - 50x + 50 Area of yard

(x + 8)(x - 2) =
x^2 - 2x + 8x - 16 = x^2 + 6x - 16 Area of pool/patio
 
   12x^2 - 50x + 50
- ( x^2 + 6x - 16)
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11x^2 - 56x + 66 ft^2  LETTER D