(Solved): 1 Use the multinomial theorem to find the coefficient of abc in the expansion of (-a +36-23c-2) ...

Expert Answer

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Multinomial Theorem:
The multinomial theorem is used to expand the power of a sum of two terms or more than two terms. The multinomial theorem is mainly used to generalize the binomial theorem to polynomials with terms that can have any number. The weighted sum of monomials can express a power (x1 + x2 + x3+ ….. + xk)n in the form x1b1, x2b2, x3b3 ….. xkbk. Where, the generalizations of binomial coefficients, which can be known as multinomial coefficients, are used to provide the weights. The corresponding multinomial series can appear with the help of multinomial distribution, which can be described as a generalization of the binomial distribution. With the help of this theorem, we can describe the result of expanding the power of the multinomial.

In order to expand an expression, the multinomial theorem provides a formula, which is described as follows:

(x1 + x2 +?+ xk)n for integer values of n

We can expand this formula in the following way:
  

Where
n = n1 + n2 + n3 + …. + nk and n! is used to describe the factorial notation for 1*2*3* …. *n