Multinomial theorem

For a nonnegative integer

n

,

(x_{1} + \dots + x_{r})^{n} = \sum_{α_{1} + \dots + α_{r} = n} \frac{n !}{α _{1} ! \dots α _{r} !} x_{1}^{α_{1}} \dots x_{r}^{α_{r}} .

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Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 70 / 4 / iii / Solution
Past exam of the mathematics course of the University of Cambridge / 2005 / ia / Paper 2 / 4F / Solution
Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3 / 11I / c / Solution
Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 105 / 1 / a / Solution
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The Multinomial Theorem is a generalization of the Binomial Theorem that describes how to expand expressions of the form \((x_1 + x_2 + \cdots + x_m)^n\), where \(x_1, x_2, \ldots, x_m\) are variables and \(n\) is a non-negative integer.

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