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Math Help - Factoring Completely

  1. #1
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    Factoring Completely

    Hello Everyone,

    I'm returning to school after a long time off, and I know this is a pretty basic question, but I can't seem to get it.

    The problem is pretty simple:

    Factor Completely
    125-27u^3

    Now I know that the cube of 125 is 5 and the cube of 27 is 3, and I'm sure that ties into here since it sounds like I need to find the GCF twice and make three parentheticals. I can't seem to make this work however, and I'm feeling foolish.

    Many Thanks!
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  2. #2
    Super Member
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    Actually, this is a difference of cubes, so you use the difference of cubes formula:
    a^3 - b^3 = (a - b)(a^2 + ab + b^2)

    So in
    125-27u^3,

    let a = 5 and b = 3u, so
    125-27u^3
    = 5^3 - (3u)^3
    = (5 - 3u)(5^2 + 5(3u) + (3u)^2)
    = (5 - 3u)(25 + 15u + 9u^2)


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  3. #3
    MHF Contributor
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    Talking

    Quote Originally Posted by croc870 View Post
    Factor Completely
    125-27u^3

    Now I know that the cube of 125 is 5 and the cube of 27 is 3...
    I think you mean that the cube of 5, 5^3, is 125 and that the cube of 3, 3^3, is 27...?

    Quote Originally Posted by croc870 View Post
    I'm sure that ties into here since it sounds like I need to find the GCF twice and make three parentheticals.
    You only need to apply the difference-of-cubes factoring formula to what is, as you have noted, equivalent to (5)^3 - (3u)^3.

    You should end up with two sets of parentheses....
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  4. #4
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    sum difference cubes

    Using ye olde Google
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