Algebraic Subtraction – Simplifying Expressions
Subtracting algebraic expressions follows a single key rule: distribute the minus sign over every term in the bracket, then collect like terms.
What Are Like Terms?
Like terms share the same variable raised to the same power.
| Like Terms | Not Like Terms |
|---|---|
| 3x and 7x | 3x and 7x² |
| 4y and −y | 5x and 5y |
| 8 and −3 (constants) | 6xy and 6x |
Distributing the Minus Sign
(5x + 3) − (2x + 1) = 5x + 3 − 2x − 1 = 3x + 2
(4x − 6) − (x − 4) = 4x − 6 − x + 4 = 3x − 2
Worked Examples
Easy
Simplify 9a − 4a: same variable → 9−4=5. Answer: 5a
Medium
(6x² + 3x − 2) − (2x² − x + 5)
= 6x² + 3x − 2 − 2x² + x − 5
= 4x² + 4x − 7
Advanced
(3a²b − 2ab + 5) − (a²b + 3ab − 7)
= 3a²b − 2ab + 5 − a²b − 3ab + 7
= 2a²b − 5ab + 12
Common Mistakes
- Forgetting to flip signs on all terms after the minus sign.
- Subtracting unlike terms (e.g., x − x² cannot be simplified further).
Key Takeaways
- Distribute the minus sign: every sign inside the bracket is reversed.
- Then group and simplify like terms.
- Only like terms can be combined.
Practice Questions
- Simplify 8m − 3m.
- Simplify (5x + 4) − (2x + 1).
- Simplify (7a² − 3a + 2) − (2a² + a − 5).
- Simplify (4xy + 3x) − (xy − x).
- Simplify (n² − 6n + 9) − (n² − 4n + 1).