Trinomial expansion

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.

The number of terms of an expanded trinomial is :$$frac{(n+2)(n+1)}{2}

Where n is the exponent to which the trinomial is raised.