1.4 Binomial_Theorem_1 - MATH 134 Binomial_Theorem_1 NAME DR CAVALIERE The Binomial Theorem gives the expansion of the binomial x y raised to any

1.4 Binomial_Theorem_1 - MATH 134 Binomial_Theorem_1 NAME...

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MATH 134 Binomial_Theorem_1 NAME:________________________________ DR. CAVALIERE The Binomial Theorem gives the expansion of the binomial yxraised to any nonnegative integer power nnkknknkkknnnnnnnyxknyxknyxnnyxnnyxnyxnyxnyx0001122110)(#1210Notice: In each term, the sum of the exponents adds to nIn each succeeding term the exponent on xdecreases by 1 and that on yincreases by 1. The coefficients in the expansion are called the binomial coefficientsand are given by!)!(!kknnkn. We observe thatknnkknnkn!)!(!. The binomial coefficient knhas a counting interpretation: kn= “The number of ways of choosing a subset of size kfrom a set of size nA plausible reason why (#) holds is that every term in the expansion of nyx : . ”.

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