If nCr denotes the number of combinations of n things taken r at a time , then the expression

If nCr denotes the number of combinations of n things taken r at a time , then the expression
binomial theorem
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binomial theorem
In elementary algebra, the binomial theorem (or binomial expansion) is describing the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial (x + y)n into a sum involving terms of the form axbyc, here exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. For example (for n = 6),
Binomial theorem for any positive integer n,
(x–y)n = nC0xn – nC1xn – 1 y + nC2xn – 2 y2 + ... + (–1)n nCn yn
Tr+1 = nCr an–rbr.

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