Question

100 POINTS!!!!

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?

Answer 1

The area of whole backyard:

a = 3x - 5

b = 4x - 10

a · b = (3x - 5) · (4x - 10) = 3x · 4x + 3x · (-10) - 5 · 4x - 5 · (-10) =

= 12x² - 30x - 20x + 50 = 12x² - 50x + 50

The area of swimming pool with patio:

a = x + 8

b = x - 2

a · b = (x + 8) · (x - 2) = x · x + x · (-2) + 8 · x + 8 · (-2) =

= x² - 2x + 8x - 16 = x² + 6x - 16

Then the area of the region they want ot cover with new grass is:

12x² - 50x + 50 - (x² + 6x - 16) = 12x² - 50x + 50 - x² - 6x + 16 =

= 11x² - 56x + 66