Developing math vocabulary
Expression
Pronunciation: ek-SPRESH-un
An expression combines numbers, variables, and operations but does not assert that two quantities are equal.
3x + 2Developing
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.
Worked example
Simplify an expression
Simplify 4x + 3 + 2x - 5.
- Combine like variable terms: 4x + 2x = 6x.
- Combine constants: 3 - 5 = -2.
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 & ArchitectsFollow the learning trail
Prerequisites, related ideas and next concepts
Learn first
Related terms
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.
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