# Examples of Algebraic Language

The **algebraic language** is one that is used to express the different relationships existing in the field of mathematics, thus showing the theorems , principles, equations and other operations.

The elements that this type of language uses are: numbers **, letters and other symbols ****( ****1,2,3; A, P, X,…; +, – X, =,…)** ; that serve to refer to **particular and general properties,** shown through different **algebraic expressions** that will facilitate the **reading and solution of mathematical problems** .

The use of **algebraic language** has allowed the advancement of the development of **mathematics** in its different branches; such as **algebra and geometry; **in a way that, without its use, this development would have been limited.

Likewise, the **algebraic language** is characterized by using **letters** that **represent numbers** , without specific value; which would indicate that the property indicated in the **algebraic expression** , is generally fulfilled whatever the particular value that is imposed on an **equation or mathematical statement** .

Thus, for example, in inequalities the **greater or lesser relation** instead of an equal one generates several answers instead of a specific one.

It may be the case, of general relations shown through **algebraic language,** where some numbers are excluded. ** For example:**

In the **algebraic expression**

**A / B + √B**

Where the value of B = 0 or the negative B’s, turn out to be exclusive; being values that you should NOT give to the letter B.

As indicated, the **algebraic language** is made up of expressions that are made up of **letters and numbers** at the same time and that are usually separated by symbols such as +, -, *, /. But, it can also contain other symbols such as (), [], {} that are used to group or separate values; leaving the expression clearly defined.

We can see the previous observation, in the following examples. Where the use or not, of the symbols (), [], {}; makes the **algebraic expression** indicate different **mathematical statements** .

Other examples of **expressions** using ** algebraic language** , below:

- 8 (- x + 5) 2 = 8 (- x + 5) (- x + 5)
- a + b + c + 4d
- m – n
- 3 (27 – 21) = 81 – 63 = 18
- k + 1
- (a + b) 2
- f (x) = 5
- y = a + bx
- Ax²- (Bx + C) = 0
- 2 {5 [(x²-4) (x + 1) -3]} = 0