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Math Help - Easier way to factor this?

  1. #1
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    Easier way to factor this?

    30x^3y-25x^2y^2-30xy^3

    i did all the work but when i got down to

    5xy(6x^2-5xy-6y^2)

    it took me forever to get the answer

    5xy(3x+2y)(2x-3y)

    is there a faster way to determine which part of 2y and 3y are negative to get the answer? It took me an hour just to find the answer to this!
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  2. #2
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    Re: Easier way to factor this?

    30x^{3}y-25x^{2}y^{2}-30xy^{3}=5xy(6x^{2}-5xy-6y^{2})=5xy(6x^{2}-9xy+4xy-6y^{2})

    How you think... well, you have to find two numbers whose sum is -5 and whose product is -36 \left ( 6 \cdot (-6) \right ): -9+4=-5 and -9\cdot 4=-36.

    I don't think there's an easier way to determine the sign of that expression (I hope that's what you asked) than the traditional one.
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  3. #3
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    Re: Easier way to factor this?

    Quote Originally Posted by cytotoxictcell View Post
    30x^3y-25x^2y^2-30xy^3

    i did all the work but when i got down to

    5xy(6x^2-5xy-6y^2)

    it took me forever to get the answer

    5xy(3x+2y)(2x-3y)

    is there a faster way to determine which part of 2y and 3y are negative to get the answer? It took me an hour just to find the answer to this!
    If your question is only "which part" is negative, it shouldn't have taken you an hour to try both:
    (3x- 2y)(2x+ 3y)= 6x^2- 5xy+ 9xy- 6y^2= 6x^2+ 4xy- 6y^2 is wrong because the sign on "2xy" is wrong. (3x+2y)(2x-3y), of course, gives 6x^2+ 4xy- 9xy- 6y^2= 6x^2- 5xy- 6y^2, the correct product.
    Last edited by HallsofIvy; November 6th 2011 at 02:23 PM.
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