Binomial - Operations On Simple Binomials

Operations On Simple Binomials

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

This is a special case of the more general formula: .

This can also be extended to when working over the complex numbers

• The product of a pair of linear binomials and is:

• A binomial raised to the nth power, represented as

can be expanded by means of the binomial theorem or, equivalently, using Pascal's triangle. Taking a simple example, the perfect square binomial can be found by squaring the first term, adding twice the product of the first and second terms and finally adding the square of the second term, to give .

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