Binomial

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In elementary algebra, a binomial is a polynomial with two terms: the sum of two monomials. It is the simplest kind of polynomial except for a monomial.

The binomial a² − b² can be factored as the product of two other binomials:

a² − b² = (a + b)(a − b).

(This is a special case of the more general formula .)

The product of a pair of linear binomials a x + b and c x + d is:

(ax + b)(cx + d) = acx² + (ad + bc)x + bd.

A binomial raised to the n^th power, represented as

(a + b)ⁿ

can be expanded by means of the binomial theorem or, equivalently, using Pascal's triangle.

[edit] Example

A simple but interesting application of the cited binomial formula is the "(m,n)-formula" for generating Pythagorean triples: for m < n, let , then a² + b² = c².

[edit] See also

• Completing the square
• Binomial distribution
• Binomial coefficient
• The list of factorial and binomial topics contains a large number of related links.

and also a binomial is a polynomial that has two term. You can use the distributive property to find the prduct of the monimial and a binomial.