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
where is a nonnegative integer and the sum is taken over all combinations of nonnegative indices and such that. The trinomial coefficients are given by
This formula is a special case of the multinomial formula for. The coefficients can be defined with a generalization of Pascal's triangle to three dimensions, called Pascal's pyramid or Pascal's tetrahedron.Properties
The number of terms of an expanded trinomial is the triangular number
where is the exponent to which the trinomial is raised.Example
An example of a trinomial expansion with is :
