Trinomial expansion

From Wikipedia, the free encyclopedia

You have new messages (last change).

In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by

(a+b+c)^n = \sum_{i,j,k} {n \choose i,j,k}\, a^i \, b^j \, c^k

where n is a nonnegative integer and the sum is taken over all combinations of nonnegative indices i, j, and k such that i+j+k = n. The coefficients are given by

{n \choose i,j,k} = \frac{n!}{i!\,j!\,k!}

This formula is a special case of the multinomial formula for m = 3. It is of some interest that the coefficients are given by a generalization of Pascal's triangle to three dimensions, called Pascal's pyramid or Pascal's tetrahedron.

Retrieved from "http://en.wikipedia.org../../../t/r/i/Trinomial_expansion.html"
In other languages