Binomial Theorem - The Binomial Theorem in Abstract Algebra

The Binomial Theorem in Abstract Algebra

Formula (1) is valid more generally for any elements x and y of a semiring satisfying xy = yx. The theorem is true even more generally: alternativity suffices in place of associativity.

The binomial theorem can be stated by saying that the polynomial sequence { 1, x, x2, x3, ... } is of binomial type.

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