We explain what algebraic language is, its origins and functions. Also, examples of algebraic expressions and what types they can be.

Table of Contents

## What is an algebraic language?

The algebraic language **is the language of mathematics** . That is, to a system of expression that uses symbols and numbers to express what we usually communicate through words , and that **allow us to formulate theorems, solve problems and express proportions or formal relationships** of a different nature.

The algebraic language was born, logically, together with algebra , the branch of mathematics that studies the relationship and combination of abstract elements according to certain rules. These elements can be numbers or quantities, but they can also be unknown values or certain numerical ranges, for which letters (known as unknowns or variables ) are used.

Originally, this field of knowledge was called *al-jabr wa l-muqabala* , that is, “the science of restoring balance”, as formulated by one of his fathers, the Persian astronomer, geographer and mathematician Al-Khuarismi. (ca. 780-ca. 850). The name came from his studying how to move a term from one side of an equation to the other, or how to add one to both sides to preserve proportion. Over time *al-jabr* came to Latin as *algeber* or *algebra* .

Seen in this way, then, the algebraic language is the language of algebra. **The written forms that said language produces are known as ****algebraic expressions** : any number, any equation are perfect examples of it. Using these types of expressions, then, we can “speak” the algebraic language, and communicate relations and operations that go far beyond the scope of mere arithmetic.

## What is an algebraic language for?

As we have said before, the algebraic language is used to build algebraic expressions, that is, **formulations in which numbers, symbols and letters are combined to express a logical and/or formal relationship** , in which some quantities are known and others are unknown.

Algebraic expressions, then, are ordered strings of these signs, in which we will find numbers, letters, and arithmetic operators. Depending on what they are, we can distinguish between, for example:

**Unknowns**(which express unknown values)**or variables**(which express non-fixed values), the latter being dependent or independent .**Arithmetic signs**(which express determined arithmetic operations).**Superscripts or powers**(which involve multiplying a number by itself a certain number of times).**Roots or radicals**(which involve dividing a number by itself a certain number of times).**Functions**(which express a dependency relationship between two values of two or more expressions).

## Examples of algebraic expressions

The following are examples of algebraic expressions:

- 19465 + 1
- 9x + 2
- 6x . 2 (4+x)
- 2×3
^{_} - 8a + 4b = c
- y – 20(x) = ½
- F(x) = 2 (A, B)
- 4 (a + b)
- 6A + 2B – C = 0
- 4
^{½}= 2 - 2y = x – 2
- 1/(y+x) . 5
- x
^{3}+ 2y^{2}+ 9 - [ 5
^{3}. (a+b) ] – 7 - 9 + 9 + 9 + 9
- 5 + (1 – y) = 3
- 84
- y – x + 1