ACoPS-proving multinomial theorem

[rakeen]

"Expand (x + y + z)2 and
(x + y + z)3 with multinomial theorem(using binomial). Think about what make the coefficients
what they are."

if we expand $(x+y+z)^2$ algeraically then we'll see that there's no binomial coefficient(yeah I know there shouldn't be.it should be trinomial coefficient.and I'm trying to find that)! Like $x^2+ y^2 + z^2 + 2xy + 2yz + 2zx$ - 1,2,1,2,1 and 2.That means we need to try something(add something and use symmetry may be!) to get those coefficients. How can I do that?

[nafistiham]

\[x+y+z=(x+y)+z\]

so, every multinomial can be turned into a binomial.

of course, it is very hard to calculate.but, if you want such kind of theorem, (i don't know if there is any or not) those calculations would also be difficult.

[rakeen]

that's what the problem asked us. To calculate x+(y+z) with binomial theorem to get trinomial and soforth.

[*Mahi*]

http://en.wikipedia.org/wiki/Multinomial_theorem