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30 October, 13:07

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.

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  1. 30 October, 13:16
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    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
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