- #1
- 6,223
- 31
Well according to what I've read
[tex](a+b+c)^n=\sum_{i,j,k} \left(
\begin{array}{c}
n\\
i,j,k
\end{array}
\right)a^i b^j c^k[/tex]
[tex]
\left(
\begin{array}{c}
n\\
i,j,k
\end{array}
\right)
=\frac{n!}{i!j!k!}[/tex]
I understand the last equation but how would I find the values for i,j and k?
for example if I have [itex](1+x+x^2)^8[/itex] how would I find the coefficient of x^3 without expanding the entire thing out?
[tex](a+b+c)^n=\sum_{i,j,k} \left(
\begin{array}{c}
n\\
i,j,k
\end{array}
\right)a^i b^j c^k[/tex]
[tex]
\left(
\begin{array}{c}
n\\
i,j,k
\end{array}
\right)
=\frac{n!}{i!j!k!}[/tex]
I understand the last equation but how would I find the values for i,j and k?
for example if I have [itex](1+x+x^2)^8[/itex] how would I find the coefficient of x^3 without expanding the entire thing out?