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Math Help - Couple binomial Things

  1. #1
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    Couple binomial Things

    First, can some tell me if I did this right, and if not, tell me what I did wrong.

    expand (x+4y)^5

    I got: x^5 + 20x^4y + 26x^3y^2 + 74x^2y^3 + 261xy^4 + 1024y^5

    Second, I've forgotten the formulas for exponential growth and decay, If someone could provide those I'd greatly appreciate it.
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  2. #2
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
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    using the binomial formula:

    <br /> <br />
\begin{gathered}<br />
  \left( {x + 4y} \right)^5  = \sum\limits_{k = 0}^5 {\left( {\begin{array}{*{20}c}<br />
   5  \\<br />
   k  \\<br /> <br />
 \end{array} } \right)} x^{5 - k} \left( {4y} \right)^k  \hfill \\<br />
   \hfill \\<br />
  where:\quad \left( {\begin{array}{*{20}c}<br />
   5  \\<br />
   k  \\<br /> <br />
 \end{array} } \right) = \frac{{5!}}<br />
{{k!\left( {5 - k} \right)!}}\quad  \hfill \\ <br />
\end{gathered} <br /> <br />
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  3. #3
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    ummm

    I used Pascal's triangle, I was wondering if my numerical coefficients are correct mostly, what you said went over my head, thanks for trying to help me anyways and still looking for exponential growth and decay formulas, they have something to do with half-life I think.
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  4. #4

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