Binomial |
: For the scientific naming of living things, see binomial nomenclature. : See binomial (disambiguation) for a list of other meanings.
In s. It is the simplest kind of polynomial.
Examples:
The multiplication of a binomial a + b with a factor c is obtained by distributivity the monomial: : 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 : (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 : a x + b quad where a and b are constants and x is a Variable.
A complex number is a binomial of the form : a + i b quad 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 x + b quad : c x + d quad : ----------- quad : a c x^2 + c b , x quad ::: a d x , + b d quad : ----------- quad : a c x^2 + (c b + a d) x + b d quad
A binomial a + b raised to the nth Exponentiation, represented as : (a + b)^n quad 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 =
*completing the square *binomial distribution *binomial coefficient. *The list of factorial and binomial topics contains a large number of related links.|
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