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Section2.6The Binomial Theorem

Here is a truly basic result from combinatorics kindergarten.

Proof
Example2.31

There are times when we are interested not in the full expansion of a power of a binomial, but just the coefficient on one of the terms. The Binomial Theorem gives that the coefficient of \(x^5y^8\) in \((2x-3y)^{13}\) is \(\binom{13}{5}2^{5}(-3)^8\).