The current area of the city park is represented by the expression 11×2 + 4x + 6. The city will expand the park this summer by a factor of 5

Question

The current area of the city park is represented by the expression 11×2 + 4x + 6. The city will expand the park this summer by a factor of 5x − 3. If one-fourth of the new park is to be wooded, which expression represents the new area of the park that is not wooded?

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    2021-09-20T22:53:56+00:00

    we have that
    the current area of the city park is 
    represented by——–> [11x² + 4x + 6]

    the new area of the city park is represented by—– >[11x² + 4x + 6]*[5x-3]
     [11x² + 4x + 6]*[5x-3]——-> [55x³+20x²+30x-33x²-12x-18]
     [55x³+20x²+30x-33x²-12x-18]=[55x³-13x²+30x+18x-18]

    the new area of the city park is represented by—->[55x³-13x²+30x+18x-18]

    we know that
    if (1/4) of the new park is to be wooded
    then 
    (3/4) of the new park  is not wooded

    therefore
    the area of the new park that 
    is not wooded is represented by–> (3/4)*[55x³-13x²+30x+18x-18]
     [41.25x³-9.75x²+22.5x+13.5]

    the answer is  [41.25x³-9.75x²+22.5x+13.5]

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