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Math Help - Using the Binomial Thm.

  1. #1
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    Using the Binomial Thm.

    Find the coefficients of x^5y^13 in the expansion of (3x - 2y)^18

    Can someone show the steps. Thanks
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  2. #2
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    Quote Originally Posted by jzellt View Post
    Find the coefficients of x^5y^13 in the expansion of (3x - 2y)^18

    Can someone show the steps. Thanks
    Can you write down the general term?
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  3. #3
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    I started by writing: 18C0 * (3x)^18 * (-2y)^0 + 18C1 * (3x)^17 * (-2y)^ 1 + ...

    Am I going about it the wrong way?
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  4. #4
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    Quote Originally Posted by jzellt View Post
    I started by writing: 18C0 * (3x)^18 * (-2y)^0 + 18C1 * (3x)^17 * (-2y)^ 1 + ...

    Am I going about it the wrong way?
    Yes you are.

    The general term is {18 \choose r} (3x)^{18 - r} (-2y)^r.

    Simplify this. Isolate the coefficient. Then see if there's a good value of r to use ....
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  5. #5
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    Thanks for your time, but I'm still not understanding what to do....
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  6. #6
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    Quote Originally Posted by jzellt View Post
    Thanks for your time, but I'm still not understanding what to do....
    Then for the moment just do the first two things and isolate the coefficient of the general term .
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