# Binomial-theorem meaning

The theorem that specifies the expansion of any power ( a + b ) m of a binomial ( a + b ) as a certain sum of products aibj , such as ( a + b )2 = a2 + 2 ab + b2 .
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The general formula for the expansion of any binomial when raised to a power that is a positive whole number; the expansion of (a + b)n: discovered by Omar Khayyám and generalized by Sir Isaac Newton (Ex.: (a + b)2 = a2 + 2ab + b2)
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The theorem that specifies the expansion of any power of a binomial, that is, ( a + b ) m. According to the binomial theorem, the first term of the expansion is xm , the second term is mxm&spminus;1 y, and for each additional term the power of x decreases by 1 while the power of y increases by 1, until the last term ym is reached. The coefficient of xm&spminus;r is m ![ r !( mr )!]. Thus the expansion of ( a + b )3 is a3 + 3 a2 b + 3 ab2 + b3 .
(mathematics) A formula giving the expansion of a binomial such as raised to any positive integer power, i.e. . It's possible to expand the power into a sum of terms of the form where the coefficient of each term is a positive integer. For example.

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