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Binomial
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For other uses, see

Binomial (disambiguation).
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In ?the sum of two

monomials?often bound by parenthesis or brackets when operated upon. It is the simplest kind of polynomial after the

monomials.

## Contents

## Operations on simple binomials

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 (ax + b) and (cx + d) is:
(ax + b)(cx + d) = acx2 + adx + bcx + bd.
A binomial raised to the nth

power, represented as
(a + b)n
can be expanded by means of the

binomial theorem or, equivalently, using

Pascal's triangle. Taking a simple example, the

perfect square binomial (p + q)2 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 p2 + 2pq + q2.
A simple but interesting application of the cited binomial formula is the "(m,n)-formula" for generating

Pythagorean triples: for m < n, let a = n2 ? m2, b = 2mn, c = n2 + m2, then a2 + b2 ...

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