Question

1. The Wilson's have a rectangular backyard with a length of 3x-8 and a width of 8x+5. Theydecide to put in a pool. The rectangular pool will have a length of 4x-5 and a width of X+3.How much of the yard is still covered by grass after the installation of the pool?

Answer 1

Length of the pool: 4x + 5

Width of the pool: x + 3

Area of the pool: length*width = (4x + 5)(x + 3) = 4x*x + 4x*3 + 5*x + 5*3 = 4x² + 12x + 5x + 15 = 4x² + 17x + 15

Length of the backyard: 3x - 8

Width of the backyard: 8x + 5

Area of the backyard: length*width = (3x - 8)(8x + 5) = 3x*8x + 3x*5 - 8*8x - 8*5 = 24x² + 15x - 64x - 40 = 24x² - 49x - 40

Area still covered by grass: Area of the backyard - Area of the pool =

= 24x² - 49x - 40 - (4x² + 17x + 15 ) =

= 24x² - 4x² - 49x - 17x - 40 - 15 =

= 20x² - 66x - 55