Multinomial theorem, in algebra, a generalization of the binomial theorem to more than two variables.
Covers set theory (integers, prime and rational numbers), algorithms (Euclidean, RSA encryption), theorems (Euler, Fermat, Chinese remainder), induction proofs (well-ordered sets, weak and strong induction), combinatorics (permutations, combinations, combinatorial proofs of the binomial theorem, Pascal's identity).
In particular, the proof of the binomial theorem and the explanation of the method of finding square roots are of this character.
The above result could be found from an inductive process, using the product rule, but the inductive step is similar to that which allows extension of the binomial theorem to all positive integers, and adds little to this presentation.
The first equality is a version of the binomial theorem.
by use of the binomial theorem.
According to the binomial theorem, the development of a given polynom can be expressed as follows: (14).
From the binomial theorem, given an expected frequency of 10%, the probability of 9 out of 10 persons reporting sprout consumption within the past week was <1/1000 (22 ).
To establish these results, he introduced transformations among the variables of the problem, using a result equivalent to the binomial theorem for integral exponents.
After a couple more questions, he said he was going to ask her one on the binomial theorem, but, as he reckoned most of his own colleagues knew nothing of it, he decided to skip it".
Bernhard Bolzano, (born Oct. 5, 1781, Prague, Bohemia, Austrian Habsburg domain [now in Czech Republic] died Dec. 18, 1848, Prague), Bohemian mathematician and theologian who provided a more detailed proof for the binomial theorem in 1816 and suggested the means of distinguishing between finite and infinite classes.
