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Math Help - multinomial?

  1. #1
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    multinomial?

    F:=F(A,B,C,D)=(A+B+C+D)^{6} and  G:=G(A,B,C,D)=(A^{2}+B+C^{2}+D)^{4}

    determine the coefficients with which the following terms appear in F and G.
    i) A^{2}BC^{2}D
    ii) A^{2}B^{2}CD
    iii) A^{2}B^{3}

    i have some lecture notes on this but would find it great help if someone could show me how,also so i could double check my answers when i get them.
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  2. #2
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    Any term in the expansion of \left( {A + B + C + D} \right)^6 appears as \frac{{6!}}{{g!h!j!k!}}A^g B^h C^j D^k where the non-negative integers g + h + j + k = 6.
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  3. #3
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    but what about an example for G when there is a power included?
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  4. #4
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    Quote Originally Posted by skystar View Post
    but what about an example for G when there is a power included?
    How about your telling us what you think it might mean.
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  5. #5
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    well for iii) and using G,

    then 4!/(4!)(4!)

    would the powers get added to one another.
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  6. #6
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    Any term in the expansion of \left( {A^2 + B + C^2 + D} \right)^4 appears as \frac{{4!}}{{g!h!j!k!}}A^{2g} B^h C^{2j} D^k where the non-negative integers g + h + j + k = 4.

    ii) cannot appear in g! Do you see why?
    iii) cannot appear in f, but it can in g! Do you see why?
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  7. #7
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    im still getting really confused as to why it cant appear. for iii in G

    i do (4!/2!3!) ((A^4)(B^3)(C^2)(D))

     =2 A^{4}B^{3}C^{2}D
    thanks
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