Developing math vocabulary

Expression

Pronunciation: ek-SPRESH-un

An expression combines numbers, variables, and operations but does not assert that two quantities are equal.

Symbols and notation3x + 2
Subject
Grade bands
Difficulty

Developing

Profession trailEngineers & Architects

Plain language

What it means

An expression combines numbers, variables, and operations but does not assert that two quantities are equal.

Formal meaning

Mathematical definition

An algebraic expression is a well-formed combination of constants, variables, operators, functions, and grouping symbols that represents a value.

Where it fits

Its place in mathematics

Expressions are the pieces evaluated, simplified, graphed, or compared inside equations and formulas.

Why it matters

The practical reason to learn it

They translate verbal relationships into a compact form that can be reused and manipulated.

InputMath ruleOutput
A value without an equals claim3x + 2 is an expression; 3x + 2 = 17 is an equation.

Worked example

Simplify an expression

Simplify 4x + 3 + 2x - 5.

  1. Combine like variable terms: 4x + 2x = 6x.
  2. Combine constants: 3 - 5 = -2.
Answer

The simplified expression is 6x - 2.

Real-life example

Where this appears

An engineer writes expressions for material cost before substituting a project size.

Common mistake

What to watch for

Trying to solve an expression as though it were an equation. An expression has no equals sign setting a condition.

Memory tip

Keep this in mind

Identify terms separated by addition or subtraction, then combine only like terms.

Little-known fact

Keep curiosity alive

Two different-looking expressions can be equivalent for every allowed value.

A profession that uses this idea

Formulas begin as expressions

Engineers assemble expressions that model cost, load, area, flow, or energy before evaluating them.

Explore Engineers & Architects

Follow the learning trail

Prerequisites, related ideas and next concepts

People behind the ideas

Related Math Heroes

François Viète

François Viète was lawyer, cryptanalyst, and algebraist. He introduced systematic letter notation for known and unknown quantities and advanced symbolic algebra.

Al-Khwarizmi

A scholar whose systematic writing on calculation and equation solving helped shape algebra and whose name became the root of the word algorithm.

Put the idea to work

Related practice