Like terms
Like terms have exactly the same variable part. For example 3x and 5x are like terms, and so are 2ab and −7ab. But 4x and 4y are not like terms because their variables differ. Only like terms can be added or subtracted.
Adding and subtracting
To add or subtract, keep the variable part and combine the coefficients.
Key idea / Key idea
3x + 5x = 8x and 7y − 2y = 5y. Add or subtract only the coefficients; the variable stays the same.
Worked example / Worked example
Simplify 6a + 2b − 4a + 5b.
Group like terms: (6a − 4a) + (2b + 5b)
= 2a + 7b.
So the simplified expression is 2a + 7b.
Multiplying and dividing
For multiplication and division we work on numbers and variables together, and apply the sign rule: same signs give +, different signs give −.
- 2 × 3x = 6x
- 4a × 3b = 12ab
- 10x ÷ 5 = 2x
- −3 × 4y = −12y
Worked example / Worked example
Simplify 2(3x + 4).
Multiply each term inside the bracket by 2:
2 × 3x + 2 × 4 = 6x + 8.
Answer: 6x + 8.
Remember / Remember
- Combine only like terms.
- Same signs → +, different signs → −.
- When expanding a bracket, multiply every term inside.