Algebra
Expressions
Simplifying expressions
20 practice questions
2 video lessons
Theory + worked examples
Theory
To simplify an expression, combine like terms — terms with the same variable raised to the same power:
- Add or subtract the coefficients.
- Combine constants separately.
- Unlike terms (different variable or power) stay separate.
\(3x\) and \(3x^2\) are not like terms — the powers differ.
Combine like terms by adding coefficients.
Which terms are alike.
Combining like terms:
\[ax+bx=(a+b)x\]
Distribute first if there are parentheses.
How to simplify
- Distribute to remove parentheses.
- Group like terms.
- Add or subtract their coefficients.
- Write the result in order.
Example 1 — Combine like terms
Simplify \(3x+5x\).
Solution
Add the coefficients.
| \(3x+5x\) | \(=\) | \(8x\) |
Example 2 — Variables and constants
Simplify \(2x+7-x-3\).
Solution
Combine \(x\)-terms and constants separately.
| \((2x-x)+(7-3)\) | \(=\) | \(x+4\) |
Example 3 — Distribute then combine
Simplify \(4(x+2)-3x\).
Solution
Distribute first, then combine.
| \(4x+8-3x\) | \(=\) | \(x+8\) |
Example 4 — Different powers
Simplify \(x^2+3x+2x^2\).
Solution
Only same-power terms combine.
| \((x^2+2x^2)+3x\) | \(=\) | \(3x^2+3x\) |
Common pitfalls
Only combine like terms — same variable and power.
Keep the sign in front of each term.
Distribute before combining when there are parentheses.
Frequently asked questions
What are like terms?
Terms with the same variable raised to the same power.
How do you combine \(3x+5x\)?
Add the coefficients: \(8x\).
Are \(x\) and \(x^2\) like terms?
No — the powers are different.
Do you distribute before combining?
Yes, remove parentheses first.
More in Expressions