Binomial theorem

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In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power (x + y)n into a sum involving terms of the form axbyc, where the coefficient of each term is a positive integer, and the sum of the exponents of x and y in each term is n. For example,

The coefficients appearing in the binomial expansion are known as binomial coefficients. They are the same as the entries of Pascal's triangle, and can be determined by a simple formula involving factorials. These numbers also arise in combinatorics, where the coefficient of xnkyk is equal to the number of different combinations of k elements that can be chosen from an n-element set.

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