Algebra guide
Simplifying Algebraic Expressions
Combine like terms, distribute carefully, cancel factors legally, and state restrictions on rational expressions.
7 min readBeginnerUpdated 2026-07-12
What you will learn
- Identify like terms
- Use distribution and factoring
- Preserve domain restrictions when canceling
Concept 1
Only like terms combine
Terms are like terms when their variable parts, including exponents, match exactly. Add or subtract only their coefficients.
Concept 2
Distribution removes grouped multiplication
Multiply every term inside the parentheses. A negative sign outside parentheses changes every sign inside.
Concept 3
Cancel factors, not terms
Factor a rational expression before canceling. Keep the restrictions from the original denominator even if a factor disappears from the simplified form.
Worked example
Simplify 2(x+3)−x
- 1Distribute 2 to obtain 2x+6−x.
- 2Combine the like x terms.
- 3No further factoring or cancellation is needed.
Answer
Common mistakes
- Combining terms with different exponents
- Distributing to only the first term
- Canceling across addition or losing denominator restrictions
Check your understanding