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Trinomial expansion
From Wikipedia, the free encyclopedia
In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by
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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.[1] The trinomial coefficients are given by
This formula is a special case of the multinomial formula for m = 3. The coefficients can be defined with a generalization of Pascal's triangle to three dimensions, called Pascal's pyramid or Pascal's tetrahedron.[2]