Algebraic Addition – Adding Like Terms
In algebra, addition works with letters as well as numbers. The key rule is that you can only add like terms — terms that have exactly the same variable raised to exactly the same power.
What Are Like Terms?
| Like terms (can be added) | Unlike terms (cannot be added) |
|---|---|
| 3x and 5x (same variable x) | 3x and 5y (different variables) |
| 4a² and 7a² (same variable, same power) | 4a² and 7a (different powers) |
| 8 and 12 (both constants) | 8 and 3x (one is a constant, one is not) |
Collecting Like Terms
To simplify an algebraic expression by addition, group like terms together and add their coefficients.
3x + 5x = (3+5)x = 8x
7a + 4b + 2a = (7+2)a + 4b = 9a + 4b
Worked Examples
Example 1 – One Variable
Simplify: 4x + 9 + 3x + 2
Group like terms: (4x + 3x) + (9 + 2) = 7x + 11
Example 2 – Two Variables
Simplify: 5a + 3b + 2a + 7b
Group: (5a + 2a) + (3b + 7b) = 7a + 10b
Example 3 – Mixed Powers
Simplify: 2x² + 3x + x² + 5x + 4
Group: (2x² + x²) + (3x + 5x) + 4 = 3x² + 8x + 4
Adding Algebraic Expressions with Brackets
When adding expressions in brackets, simply remove the brackets (the sign in front applies to every term inside) and then collect like terms.
(3x + 4) + (5x + 2) = 3x + 4 + 5x + 2 = 8x + 6
Key Takeaways
- Only like terms (same variable, same power) can be added.
- Add the coefficients; keep the variable part unchanged.
- Constants are like terms with each other.
- When adding bracketed expressions, remove brackets then collect like terms.
Practice Questions
- Simplify 6x + 4x.
- Simplify 3a + 5b + 2a + b.
- Simplify 4x² + 3x + 2x² + 7x + 1.
- Add (2x + 5) + (4x + 3).
- Add (3a + 2b + 1) + (a + 4b + 5).