Binomial theorem

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 a x^b y^c, 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,

The coefficient a in the term of a x^b y^c is known as the binomial coefficient ${\displaystyle {\tbinom {n}{b}}}$ or ${\displaystyle {\tbinom {n}{c}}}$ (the two have the same value). These coefficients for varying n and b can be arranged to form Pascal's triangle. These numbers also arise in combinatorics, where ${\displaystyle {\tbinom {n}{b}}}$ gives the number of different combinations of b elements that can be chosen from an n-element set.

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