Why simplify?
A long expression like 3x + 5 − x + 2(x + 4) is harder to read and use than its simplified version 4x + 13. To simplify means to write an equivalent expression that is as short as possible.
Step 1: Remove brackets
Use the distributive property: multiply every term inside the brackets by the number outside.
- 2(x + 4) = 2x + 8
- −3(y − 5) = −3y + 15 (a negative times a negative is positive)
- −(a + 6) = −a − 6
Step 2: Combine like terms
Group like terms and add or subtract their coefficients.
Example: 3x + 5 − x + 2(x + 4)
- Remove brackets: 3x + 5 − x + 2x + 8
- x terms: 3x − x + 2x = 4x
- Constants: 5 + 8 = 13
- Result: 4x + 13
Keep track of signs
The sign in front of a term moves with it. It helps to rewrite subtraction as adding a negative:
7a − 3b − 2a + 5b = 7a + (−3b) + (−2a) + 5b
- a terms: 7a − 2a = 5a
- b terms: −3b + 5b = 2b
- 5a + 2b
Multiplying terms
When multiplying (not adding) terms, multiply coefficients and variables separately:
- 3x × 4 = 12x
- 2a × 5b = 10ab
- 4x × 3x = 12x²
Checking with substitution
Two expressions are equivalent if they give the same value for any x. Test with x = 2:
- Original: 3(2) + 5 − 2 + 2(2 + 4) = 6 + 5 − 2 + 12 = 21
- Simplified: 4(2) + 13 = 21 ✓
Worked examples
Example 1: Simplify 6m + 4 − 2m − 9.
4m − 5.
Example 2: Simplify 5(2x − 1) − 3x.
10x − 5 − 3x = 7x − 5.
Example 3: Simplify 4(a + 2) − 2(a − 3).
4a + 8 − 2a + 6 = 2a + 14.
Common mistakes
- Distributing to only the first term: 2(x + 4) ≠ 2x + 4.
- Forgetting the negative when distributing a negative: −2(a − 3) = −2a + 6, not −2a − 6.
- Combining unlike terms: 3x + 4 ≠ 7x.
- Losing the sign when moving terms around.
Try it yourself
- 9y − 4y + 2
- 3(x + 5) + 2x
- 8 − 2(n + 1)
- 2(3a − b) + 4(a + 2b)
- x² + 3x − 2x² + x
Answers: 1) 5y + 2 2) 5x + 15 3) 6 − 2n 4) 10a + 6b 5) −x² + 4x
Quick recap
- Simplify by removing brackets, then combining like terms.
- Use the distributive property carefully with negatives.
- Check that the result is an equivalent expression by substituting.