Combining like terms
Only terms with the same variable and power can be added together.
The common mistake
Adding unlike terms, e.g. 3x + 2x² = 5x³ or 4x + 3 = 7x.
Instead: Group terms by exactly matching variable parts (x with x, x² with x², numbers with numbers), then add their coefficients.
Worked example with Guide me
Simplify 5x + 3 − 2x + 4x² − 1.
- Sugar · Which terms have plain x?Student · 5x and −2x, which make 3x.
- Sugar · Which are just numbers?Student · 3 and −1, which make 2.
- Sugar · Anything left?Student · 4x² stays on its own.
Answer: 4x² + 3x + 2
Try 3 practice questions
1. Simplify 7a − 3b + 2a + b.
Show answer
9a − 2b
2. Simplify x² + 3x − x² + 5.
Show answer
3x + 5
3. Simplify 6y + 4 − 6y.
Show answer
4
Quick answers
- What is the most common mistake with combining like terms?
- Adding unlike terms, e.g. 3x + 2x² = 5x³ or 4x + 3 = 7x.
- How do I get combining like terms right?
- Group terms by exactly matching variable parts (x with x, x² with x², numbers with numbers), then add their coefficients.
- Can you show a worked example?
- Simplify 5x + 3 − 2x + 4x² − 1. 4x² + 3x + 2
Related concepts
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