# Math Help - multinomial?

1. ## 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.

2. 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 $g + h + j + k = 6$.

3. but what about an example for G when there is a power included?

4. Originally Posted by skystar
but what about an example for G when there is a power included?

5. well for iii) and using G,

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

would the powers get added to one another.

6. 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?

7. 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