that would be the area of the yard less the area of the patio. So,
(2x+3x)(3x-5)-(x+2)^2
or, assuming a typo,
(2x+3)(3x-5)-(x+2)^2
= (6x^2-x-15)-(x^2+4x+4)
= 5x^2-5x-19
(2x+3x)(3x-5)-(x+2)^2
or, assuming a typo,
(2x+3)(3x-5)-(x+2)^2
= (6x^2-x-15)-(x^2+4x+4)
= 5x^2-5x-19
The given dimensions of the backyard are 2x + 3x by 3x - 5, which means the length is 2x + 3x and the width is 3x - 5.
Area of the backyard = length * width = (2x + 3x) * (3x - 5) = 5x * (3x - 5) = 15x^2 - 25x
The dimensions of the square patio are given as x + 2, thus the area of the patio would be:
Area of the patio = side length * side length = (x + 2) * (x + 2) = (x + 2)^2 = x^2 + 4x + 4
To find the area of grass that will be left in the backyard, we subtract the area of the patio from the area of the backyard:
Area of grass = Area of backyard - Area of patio
Area of grass = (15x^2 - 25x) - (x^2 + 4x + 4)
Area of grass = 15x^2 - 25x - x^2 - 4x - 4
Area of grass = 14x^2 - 29x - 4
Therefore, the expression for the area of grass that will be left in the backyard after the patio is built is 14x^2 - 29x - 4.