structural:summarization
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) into a sum involving terms of the form ax y, 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 3 y + 6 x 2 y 2 + 4 x y 3 + y 4. {\displaystyle (x+y)^{4}=x^{4}+4x^{3}y+6x^{2}y^{2}+4xy^{3}+y^{4}.}

The coefficient a in the term of ax y is known as the binomial coefficient (n b) {\displaystyle {\tbinom {n}{b}}} or (n c) {\displaystyle {\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 (n b) {\displaystyle {\tbinom {n}{b}}} gives the number of different combinations (i.e. subsets) of b elements that can be chosen from an n -element set. Therefore (n b) {\displaystyle {\tbinom {n}{b}}} is usually pronounced as " n choose b ".