binomial expansion


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binomial expansion

[bī′nō·mē·əl ik′span·shən]
(mathematics)
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Example 1 shows a standard binomial expansion and clarifies how the like terms appear.
The binomial expansion is utilized to predict the probability of certain combinations of events when there are several different ways in which the set of events can occur.
To illustrate use of the binomial expansion in probability, students again work in small groups (we use groups of four).
(It does not matter that this is not connected to any specific mathematical relationship, as with binomial expansions; we are simply playing with the numbers here.) The Pascal Trapezium becomes:
Then the largest coefficient in the binomial expansion of [(dx + 1).sup.n] is
Moody's modeled the transaction using a cash flow model based on the Binomial Expansion Technique, as described in "Moody's Global Approach to Rating Collateralized Loan Obligations."
Moody's modeled the transaction using a cash flow model based on the Binomial Expansion Technique, as described in Section 2.3 of the "Moody's Global Approach to Rating Collateralized Loan Obligations," published in December 2015.
Then, students are given four or five notebooks, written on various topics such as patterns on binomial expansions and series approximations.
Milan Pahor introduces and justifies techniques for finding the largest coefficient of binomial expansions. This article presents a series of proofs which, since binomial coefficients are commonly encountered in the algebra and probability sections of our courses, may be of interest to our students.
A brief investigation led me quickly down the path of binomial expansions, parametric equations, the concept of nesting, and spinners/scroll bars in an Excel spreadsheet.