Hi my name is murray and I am a highschool student. Could you please state and explain the multinomial theorem (I already know the binomial theorem etc, to give you an idea of where i am) Thanks alot Hi Murray,
Since you know the binomial theorem I would start with trinomials. You should expand (a + b + c)^{2} and (a + b + c)^{3} by multiplying them out to see how the coefficients are constructed. =(a + b + c)(a + b + c) = a^{2} + b^{2} + c^{2} + 2ab + 2ac + 2bc (a + b + c)^{3} = (a + b + c)(a + b + c)(a + b + c) = a^{3} + b^{3} + c^{3} + 3a^{2}b + 3a^{2}c + 3ab^{2} + 3b^{2}c + 3 ac^{2} + 3 bc^{2} + 6 abc If you think of these two examples as (a + b + c)^{n} then each of the term is a constant times a^{p}b^{q}c^{r} where p + q + r = n. In the first case n = 2 and in the second n = 3. In the general case The notation means that you form a sum of all possible terms of the form a^{p}b^{q}c^{r} where p + q + r = n with each term having a coefficient of
The multinomial theorem is of the same form. Harley
