Binomial - AbsoluteAstronomy.com

In algebra

Algebra

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...

, a binomial is a polynomial

Polynomial

In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...

with two terms —the sum of two monomial

Monomial

In mathematics, in the context of polynomials, the word monomial can have one of two different meanings:*The first is a product of powers of variables, or formally any value obtained by finitely many multiplications of a variable. If only a single variable x is considered, this means that any...

s—often bound by parenthesis or brackets when operated upon. It is the simplest kind of polynomial after the monomial

Monomial

The binomial can be factored as the product of two other binomials:

This is a special case of the more general formula:

The product of a pair of linear binomials and is:

A binomial raised to the n^th power
Exponentiation
Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n...

, represented as

can be expanded by means of the binomial theorem

Binomial theorem

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 n into a sum involving terms of the form axbyc, where the exponents b and c are nonnegative integers with , and the coefficient a of...

or, equivalently, using Pascal's triangle

Pascal's triangle

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician, Blaise Pascal...