Other Definitions binomial (dict)
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Binomial - For the scientific naming of living things, see binomial nomenclature.
In elementary algebra, a binomial is a polynomial with two terms: the sum of two monomials. It is the simplest kind of polynomial. In biology, Binomial nomenclature is a naming convention for all living things. Examples: -
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The product of a binomial a + b with a factor c is obtained by distributing the monomial: -
The product of two binomials a + b and c + d is obtained by distributing twice: -
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The square of a binomial a + b is -
and the square of the binomial a - b is -
The binomial can be factored as the product of two other binomials: -
A binomial is linear if it is of the form -
where a and b are constants and x is a variable. A complex number is a binomial of the form -
where i is the square root of minus one. The product of a pair of linear binomials a x + b and c x + d is: -
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A binomial a + b raised to the nth power, represented as -
can be expanded by means of the binomial theorem or Pascal's triangle. Pascal's triangle is not good to use with large numbers but as a rule of thumb will suffice where the power does not exceed 7. See also:
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