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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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