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

### characteristics

It is necessary to clarify that when we talk about ‘mathematical elements’ we are referring to **numbers or to 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, nor involved in any other operation.

Thus, it can be affirmed that the **distinction between the members is made by a sign ‘+’ or by a ‘-‘** , and then A + B is a binomial, but neither A * B nor A ^ B (these would constitute a single member ).

Each of the members of a binomial is called a **‘term’. **With the binomials special operating criteria apply. The operation that is most frequently applied in binomials is that of **common factor** .

**When the two terms of a binomial are multiplied or divided by the same, the multiplication can be one** . Thus, double A plus double B equals twice (A + B). This happens because in the binomials the distributive (and associative) property of multiplication is applied, 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 the **square of the binomial** , where (A + B) ^{2} = (A _{2} + 2 * A * B + B _{2} ). A binomial often makes solving equations difficult, **Newton’s formula** often solves this difficulty.

Today, the idea of ’binomial’ has surpassed the world of algebra and mathematics. The **combination of two names in the framework of any human activity** is called binomial . Everything that is made up of someone’s name and that of another person is a binomial, and it is applied above all in the political world, also in sports and art 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**(actor couple)**John Kennedy – Lyndon Johnson**(United States Presidential Formula)**Mickey and Minnie**(fictional characters from the beginning of cartoons)**Juan Domingo Perón – María Estela Martínez de Perón**(presidential formula)**Tristan and Isolde**(characters from an ancient legend, who gave name to the famous Wagner opera)**Don Quixote and San Panza**(fictional characters from the book of Cervantes)**The cow and the chick**(characters from a cartoon)**Mick Jagger and Keith Richards**(musicians from the same band, Rolling Stones)**The Fat and the Skinny**(comic characters from the silent film era