Binomial

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 $$a^2 - b^2 can be factored as the product of two other binomials::$$a^2 - b^2 = (a + b)(a - b). (This is a special case of the more general formula $$a^{n+1} - b^{n+1} = (a - b)sum_{k=0}^{n} a^{k},b^{n-k}.)

The product of a pair of linear binomials "a x + b" and "c x + d" is::$$ (a x + b)(c x + d) = a c x^2 + (a d + b c) x + b d.

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.

Example

A simple but interesting application of the cited binomial formula is the "(m,n)-formula" for generating Pythagorean triples: for "m < n", let $$a=n^2-m^2, b=2mn, c=n^2+m^2, then $$a^2+b^2=c^2.

See also

*Completing the square
*Binomial distribution
*Binomial coefficient
* Binomial-QMF (Daubechies Wavelet Filters)
*The list of factorial and binomial topics contains a large number of related links.

External links

* [http://www.allmathwords.org/binomial.html Binomial] All Math Words Encyclopedia for grades 7-10.