Easy approach to the binomial theorem

This is more of a refresher for people that learned combinations and permutations but then later forgot the formula [like me]. How many combinations of wins are there in 12 football games? If so, could you do another explanation in that field, I have been reading your posts and this one and the ones on e and ln are terribly interesting. That is one of the secrets of success in life. Smullyan in his book B. He drew a right triangle on the board with squares on the hypotenuse and legs and observed the fact the the square on the hypotenuse had a larger area than either of the other two squares.

Then he asked, "Suppose these three squares were made of beaten gold, and you were offered either the one large square or the two small squares. Which would you choose? Both groups were equally amazed when told that it would make no difference.

The theorem is of fundamental importance in Euclidean Geometry where it serves as a basis for the definition of distance between two points. Below is a collection of approaches to proving the theorem. Many of the proofs are accompanied by interactive Java illustrations. Remark The statement of the Theorem was discovered on a Babylonian tablet circa B.

Binomial Theorem

Elements furnish the first and, later, the standard reference in Geometry. In fact Euclid supplied two very different proofs: The Theorem is reversible which means that its converse is also true.

Euclid was the first I. In the Foreword, the author rightly asserts that the number of algebraic proofs is limitless as is also the number of geometric proofs, but that the proposition admits no trigonometric proof. In all likelihood, Loomis drew inspiration from a series of short articles in The American Mathematical Monthly published by B.

Counting possible variations in calculations derived from the same geometric configurations, the potential number of proofs there grew into thousands. For example, the authors counted 45 proofs based on the diagram of proof 6 and virtually as many based on the diagram of 19 below.

In all, there were "shorthand" proofs. I must admit that, concerning the existence of a trigonometric proof, I have been siding with with Elisha Loomis until very recently, i. Actually, for some people it came as a surprise that anybody could doubt the existence of trigonometric proofs, so more of them have eventaully found their way to these pages.So my question is whether it possible to recover this expression from the binomial-like expansion and if it possible please give me some hints on a research or summary about common name and properties of binomial-like expansions, which properties should have two operations so that their combination gives binomial-like formula etc.

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Easy teach program fractions activities, test point method for inequalities, mathematic solving, negative polynomials. A binomial is a polynomial with exactly two terms. Multiplying out a binomial raised to a power is called binomial expansion.

Your pre-calculus teacher may ask you to use the binomial theorem to find the coefficients of this expansion. Expanding many binomials takes a rather extensive application of.

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