Expression (mathematics)

In mathematics, an expression is a mathematical object that is not an equation or other type of formula (such as an inequality).

The equation ${\displaystyle 7x-5=2}$ describes a relation between two expressions, ${\displaystyle 7x-5}$ and ${\displaystyle 2}$.

Equation versus expression

The term "equation" is often incorrectly used to talk about expressions, especially more complex ones, but an equation must have an equals sign. For example, a quadratic function is given by an equation such as

${\displaystyle f(x)=2x^{2}+3x+1}$

People will sometimes call ${\displaystyle 2x^{2}+3x+1}$ the "equation" of ${\displaystyle f(x)}$. In formal mathematics, this is incorrect: it is only a quadratic expression. Only the full statement, with ${\displaystyle f(x)=}$ included, is the equation of the function.

The difference between expressions and equations or formulae is similar to the difference between parts of speech and sentences in natural language. Expressions and relations combine to make a formula the same way that nouns or noun phrases and verbs make a sentence.