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:

  1. 8 (- x + 5) 2 = 8 (- x + 5) (- x + 5)
  2. a + b + c + 4d
  3. m – n
  4. 3 (27 – 21) = 81 – 63 = 18
  5. k + 1
  6. (a + b) 2
  7. f (x) = 5
  8. y = a + bx
  9. Ax²- (Bx + C) = 0
  10. 2 {5 [(x²-4) (x + 1) -3]} = 0

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