NationMaster - Encyclopedia: Binomial

In elementary algebra, a binomial is a polynomial with two terms: the sum of two monomials. It is the simplest kind of polynomial except for a monomial. Elementary algebra is a fundamental and relatively basic form of algebra taught to students who are presumed to have little or no formal knowledge of mathematics beyond arithmetic. ... In mathematics, a polynomial is an expression in which constants and variables are combined using only addition, subtraction, multiplication, and positive whole number exponents (raising to a power). ... In mathematics, a monomial is a particular kind of polynomial, having just one term. ...

Examples

$a + b quad$
$x+3 quad$
${x over 2} + {x^2 over 2}$
$v t - {1 over 2} g t^2$

The product of a binomial with a factor c is obtained by distributing the monomial:43 In mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalises the distributive law from elementary algebra. ...

$c (a + b) = c a + c b$

The product of two binomials a + b and c + d is obtained by distributing twice:

$(a + b)(c + d) = (a + b) c + (a + b) d$

$= a c + b c + a d + b d quad$ .

The square of a binomial a + b is In algebra, the square of x is written x2 and is defined as the product of x with itself: x × x. ...

$(a + b)^2 = a^2 + 2 a b + b^2 quad$

and the square of the binomial a - b is

$(a - b)^2 = a^2 - 2 a b + b^2. quad$

The binomial $a 2 - b 2$ can be factored as the product of two other binomials:

$a^2 - b^2 = (a + b)(a - b). quad$

A binomial is linear if it is of the form The word linear comes from the Latin word linearis, which means created by lines. ...

$a x + b quad$

where a and b are constants and x is a variable. In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. ... In computer science and mathematics, a variable (sometimes called a pronumeral) is a symbol denoting a quantity or symbolic representation. ...

A complex number is a binomial of the form In mathematics, a complex number is a number of the form where a and b are real numbers, and i is the imaginary unit, with the property i 2 = âˆ’1. ...

$a + i b quad$

where i is the square root of minus one. In mathematics, a square root of a number x is a number whose square (the result of multiplying the number by itself) is x. ...

The product of a pair of linear binomials a x + b and c x + d is:

$(a x + b)(c x + d) = a c x^2 + (a d + b c) x + b d !,$

A binomial a + b raised to the n^th power, represented as In mathematics, exponentiation (frequently known colloquially as raising a number to a power) is a process generalized from repeated (or iterated) multiplication, in much the same way that multiplication is a process generalized from repeated addition. ...

$(a + b)^n quad$

can be expanded by means of the binomial theorem or, equivalently, using Pascal's triangle. In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. ... 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 The first six rows of Pascals triangle In mathematics, Pascals triangle is a geometric arrangement of the binomial coefficients in a triangle. ...

Category: Algebra Completing the square is an algebra technique, also used in many types of calculus. ... In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. ... In mathematics, particularly in combinatorics, the binomial coefficient of the natural number n and the integer k is the number of combinations that exist. ... This is a list of factorial and binomial topics, by Wikipedia page. ...

Results from FactBites:

Binomial distribution - Wikipedia, the free encyclopedia (733 words)
	In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p.
	The binomial distribution is the basis for the popular binomial test of statistical significance.
	The number of HIV-positives you pick is a random variable X which follows a binomial distribution with n = 500 and p =.05.

Binomial - Wikipedia, the free encyclopedia (242 words)
	In elementary algebra, a binomial is a polynomial with two terms: the sum of two monomials.
	The square of a binomial a + b is
	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.

More results at FactBites »

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