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.
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