Binomial Theorem Nomenclature ```Name: Bill G. Status: student Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: I am writing a paper about the binomial theorem and I am troubled by certain nomenclature. For example, the expression (a + b) to the power of n is referred to as a binomial. Yet, when expanded, it produces a polynomial. It would be convenient if I could use the generic term binomial throughout my paper (as is done in many textbooks) to refer to the compact form or the expanded version. But, I do not feel comfortable doing this. Can you provide me with a justification for doing so? For example, is there a general rule stating that any expression can always be referred to based on the way it appears when written in the most compact form? Replies: The formal definition of a polynomial, Pn(X), is: Pn(X) = An*X^n + An-1*X^n-1 + ... + A1*X + Ao. Some of the coefficients may equal zero. The polynomial may also be compound, that is: Pn,m(X,Y) = [An*X^n]*[Bm*Y^m] + ... + Ao*Bo. That X and/or Y can be expressed as a polynomial itself X = (a+b) in your case is not at issue. So polynomial refers to the highest value of the exponents 'n' and 'm' that appears in Pn,m(X,Y). Vince Calder Click here to return to the Mathematics Archives

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