A family has a rectangular back yard that measures 5x+4 by 3x-2 they are building a square patio with side lengths that measure x+3. write an expression for the area of grass that will be left in the back yard after the patio is built. show your work.

Answer: 14x² - 4x - 17

Step-by-step explanation:

The formula for determining the area of a rectangle is expressed as

Area = length * width

The rectangular back yard measures 5x + 4 by 3x - 2. This means that the area of the rectangular back yard would be

Area = (5x + 4) (3x - 2)

Area = 15x² - 10x + 12x - 8

= 15x² + 2x - 8

The formula for determining the area of a square is expressed as

Area = length²

Length of square patio = x + 3

Area of square patio = (x + 3) (x + 3)

= x² + 3x + 3x + 9

= x² + 6x + 9

The expression for the area of grass that will be left in the back yard after the patio is built is

15x² + 2x - 8 - (x² + 6x + 9)

= 15x² + 2x - 8 - x² - 6x - 9

= 15x² - x² + 2x - 6x - 8 - 9

= 14x² - 4x - 17