Binomial
In
elementary algebra, a
binomial is a
polynomial with two terms: the sum of two monomials. It is the simplest kind of polynomial.
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 square, binomial distribution, binomial coefficient.