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