The term ‘**binomial**‘corresponds to the language of algebra and identifies one of the several elements with which one usually operates.

In particular, a binomial is a combination of two mathematical elements (called members), within the framework of an equation or a relationship between quantities or structures. For instance: *(34 * A + B / 23); 1/6 * (A + B) ^{3}; ½ (5 + 14 * G)*.

### Characteristics of a binomial

It is necessary to clarify that when talking about ‘**mathematical elements**‘is referring to numbers or unknowns that may eventually be replaced by numbers.

However, another central distinction must be made: a binomial always contains two members added or subtracted from each other, and not multiplied or divided, or involved in any other operation.

Thus, it can be stated that the distinction between the members is made by a ‘+’ sign or by a ‘-‘, and then A + B is a binomial, but not A * B or A ^ B (these would constitute a single member ).

Each of the members of a binomial is called ‘**finished**‘. Special operating criteria apply with the binomials. The operation that is most frequently applied to binomials is that of a common factor.

When the two terms of a binomial are multiplied or divided by the same, the multiplication can be a single one. Thus, twice A plus twice B equals twice (A + B). This happens because in binomials the distributive (and associative) property of multiplication applies, which means that if a number multiplies a binomial it can also multiply each of its members separately (and the same happens in reverse) .

The same does not happen in the case of powers, in that case the question is somewhat more complex: the square of the sum of A and B is not equal to the square of each of them separately. The power N of the sum between A and B will be A ^ N + B ^ N, but between those two terms there will be a sum of N-1 terms.

The most frequent case is that of **square of the binomial**, where (A + B)^{2 }= (A_{2} + 2 * A * B + B_{2}). A binomial often makes it difficult to solve equations, Newton’s formula often solves this difficulty.

Today, the idea of ’binomial’ has overtaken the world of algebra and mathematics. The combination of two names in the framework of any human activity is called a binomial. Everything that is made up of someone’s name and that of another person is a binomial, and it applies above all in the political world, also in sports and artistic or entertainment.

### Examples of binomials

**Algebraic binomials**

- (34 * A + B / 23)
- (12 – 263/3)
- ½ (5 + 14 * G)
- (43 A + 1/3 * B)
^{2} - (114 + 42)
^{3} - (21 B – A)
- (41
^{2 }– 5A^{2}) - (1/9 – 1/5)
- (5 * 10 ^
^{9.61 }– 3.5 * 10 ^^{5.41}) - 1/6 * (A + B)
^{3}

**Binomials of people or characters**

**Carlos Gardel and Alfredo Le Pera**(singer and composer of tangos)**Brad Pitt and Angelina Jolie**(couple of actors)**John Kennedy – Lyndon Johnson**(United States presidential formula)**Mickey and minnie**(fictional characters from early cartoons)**Juan Domingo Perón – María Estela Martínez de Perón**(presidential formula)**Tristan and Isolde**(characters from an ancient legend, which gave its name to Wagner’s famous opera)**Don Quixote and San Panza**(fictional characters from Cervantes’s book)**The cow and the chick**(cartoon characters)**Mick Jagger and Keith Richards**(musicians from the same band, Rolling Stones)**The fat and the skinny**(comic characters from the silent movie era)