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 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? 6x2 – 55x + 104 ft2 x2 + 6x – 16 ft2 11x2 – 56x + 66 ft2 12x2 – 50x + 50 ft2

Answer 1

the region they need to cover is
the region of the backyard minus the region of the swimming pool.
the region of the backyard is its length times its width. ( the region of a rectangular)
the region of the backyard is:
$(3x - 5) \times (4x - 10) = \\ {12x}^{2} - 30x - 20x + 50 = \\ 12x {}^{2} - 50x + 50$
the region of the swimming pool is its length times its width. ( the region of a rectangular)
the region of the swimming pool is:
$(x + 8) \times (x - 2) = \\ {x}^{2} - 2x + 8x - 16 = \\ {x}^{2} + 6x - 16$
the region they need to cover is:
$(12x {}^{2} - 50x + 50) - ( {x}^{2} + 6x - 16) = \\ 12x {}^{2} - 50x + 50 - x {}^{2} - 6x + 16 = \\ 11x {}^{2} - 56x + 66$
So; the answer is: 11x^2 - 56x + 66