A binomial is an algebraic expression with exactly two terms, such as a + b.
Binomials are the building blocks of polynomial algebra. The sum or difference of two monomials forms a binomial. Binomials are central to the Binomial Theorem, which describes the expansion of powers of a binomial (a + b)โฟ. Binomial expansions produce binomial coefficients arranged in Pascal's Triangle. Binomials appear in probability (binomial distribution), combinatorics, and algebra.
The Binomial Theorem was known to ancient mathematicians for small powers. Persian mathematician Al-Karaji described the binomial expansion and Pascal's Triangle in the 10th century. The theorem was generalized to any real exponent by Isaac Newton in 1665. The binomial coefficient notation was introduced by Andreas von Ettingshausen in 1826.