Expansion of (a+b+c)^n

Is there a formula for the expanstion of (a+b+c) power n?
If yes, how to arrive at that formula?
What are the basic steps?

Ans : 
For m terms to the nth power, m >= 1 and n >= 0,

u(*,0) = 1
u(0,n+1) = 0
u(1,n) = 1
u(2,n) = n+1
u(m,1) = m
u(m,2) = m*(m+1)/2
u(m+1,n+1) = u(m+1,n) + u(m,n+1)

That last equation looks likes the recurrence relation for Pascal's triangle, so there's a close relationship there.
u(m,n) = C(m+n-1,n)  where C(x,y) = x!/(y! * (x-y)!)
u(m,n) = (m+n-1)!/(n! * (m+n-1-n)!) = (m+n-1)!/(n! * (m-1)!)


Let's check it.  Remember that 0! = 1
u(1,1) = 1     1!/(1!*0!) = 1
u(2,1) = 2     2!/(1!*1!) = 2
u(n,1) = n     n!/(1! * (n-1)!) = n
u(1,2) = 1    2!/(2! * 0!) = 1
u(2,2) = 3    3!/(2! * 1!) = 3
u(n,2) = n*(n+1)/2  (n+1)!/(2! * (n-1)!) = n*(n+1)/2
u(2,n) = n+1   (n+1)!/(n! * 1!) = n+1

So (a+b+c+...)^n with m variables has (m+n-1)!/(n! * (m-1)!) distinct terms

Ans 2 :
http://mathforum.org/library/drmath/view/51601.html

Ans 3 :

http://mathworld.wolfram.com/MultinomialCoefficient.html
http://en.wikipedia.org/wiki/Multinomial_theorem