Concept# Binomial theorem

Summary

In elementary algebra, the binomial theorem (or binomial expansion) describes 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, where the 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 = 4,
(x+y)^4 = x^4 + 4 x^3y + 6 x^2 y^2 + 4 x y^3 + y^4.
The coefficient a in the term of axbyc is known as the binomial coefficient \tbinom{n}{b} or \tbinom{n}{c} (the two have the same value). These coefficients for varying n and b can be arranged to form Pascal's triangle. These numbers also occur in combinatorics, where \tbinom{n}{b} gives the number of different combinations of b

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Ali Chekir, Mohamed Slim Slama

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