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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:
The product of a binomial a + b with a factor c is obtain by distributing the monomial:
The product of two binomials a + b and c + d is obtained by distributing twice:
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:
A binomial a + b raised to the nth power, represented as
can be expanded by means of the binomial theorem.
See also: completing the squareCompleting the square is a technique of elementary algebra wherein an expression : is replaced by one of the form : Specifically, we have : See quadratic equation. Example A simple example is this. Now, consider the problem of finding this antiderivative:, binomial distributionIn mathematics, the binomial distribution is a discrete probability distribution which describes the number of successes in a sequence of n independent yes/no experiments, each of which yielding success with probability p''. Such a success/failure experim, binomial coefficientIn mathematics, in particular in combinatorics, the binomial coefficient of the natural number n and the integer k is defined to be the natural number : and : (Here m denotes the factorial of m . The binomial coefficient of n and k is also written as C n.