Algebraic expressions - what are these expressions and when do we use them?

Algebraic expressions consist of one or more algebraic symbols joined by action signs. How are algebraic expressions structured? When can we use them?

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1. What are algebraic expressions?

An algebraic expression is an expression consisting of letters and numbers joined by action signs and parentheses.

Examples of algebraic expressions include:

  • n;
  • 8 (2 + 5x);
  • 3;
  • x + 4y;
  • 2y
  • 4 + √9.

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However, algebraic expressions are not notations consisting of algebraic symbols, but meaningless, such as ᵃ - (, etc., expressions in which symbols of a function or relation are involved (e.g. a = b). We usually assume that these expressions have a finite length, so they cannot be continued fractions.

Some authors consider only algebraic numbers in algebraic expressions.

What are monomials in algebraic expressions? These are numbers and letters connected by the multiplication sign. We also distinguish similar monomials that differ only in the numerical coefficient.

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2. Rational and irrational expressions

If there is no power with a non-integer exponent in an algebraic expression (also a root of a degree other than 1 / k, k ∈ ℤ {0}) then it is a rational expression. Otherwise, the expression is irrational.

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3. Application of algebraic expressions

We use these expressions to record rules (formulas) for calculating quantities. Good examples are the formulas for the surface areas of figures, volume of solids or the laws of physics, such as the formula for acceleration.

In computer science, a similar (though slightly broader) concept of an arithmetic expression is used.

Some believe that a mathematical expression that does not contain variables is an arithmetic expression, and that not containing them is an algebraic expression.

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