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Math Help - binomial theorem

  1. #1
    chu
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    binomial theorem

    Find the 4th term of (x-3)8 (to the 8th power).

    This is all I have for the question. Is this enough info to work this problem?

    Thanks in advance.
    Chu
    Last edited by chu; October 14th 2008 at 11:14 PM. Reason: Adding Importance
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  2. #2
    Flow Master
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    Quote Originally Posted by chu View Post
    Find the 4th term of (x-3)8 (to the 8th power).

    This is all I have for the question. Is this enough info to work this problem?

    Thanks in advance.
    Chu
    Not quite .....

    The (r+1)th term (going in increasing powers of x) is ^8 C_r \, x^r (-3)^{8-r}.

    The (r+1)th term (going in decreasing powers of x) is ^8 C_r \, (-3)^r x^{8-r}.

    The answer will depend on which way you do it.
    Last edited by mr fantastic; October 15th 2008 at 04:14 PM. Reason: Clarified
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  3. #3
    chu
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    More info

    I have more info now: problem with multiple choice answers. I'm still not sure A, B, C, D. Thanks Flow Master

    binomial theorem-math-problem-1.jpg
    Last edited by chu; October 15th 2008 at 02:50 PM. Reason: Photo is to small
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  4. #4
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    There is a debate as to how one numbers the terms in a binominal expansion.
    So much so, that in the US we have pretty much agreed not to use that terminology in contest questions.

    But given you options, it is clear that Mr.F is correct you need to use the descending option.
    \left( {x - 3} \right)^8  = \sum\limits_{k = 0}^8 { {8 \choose k} x^{8 - k} \left( { - 3} \right)^k } so k = 3 give the term.
    So the answer is either a or b.
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