Definition: Like terms are terms that have exactly the same variables raised to the same powers, so only their coefficients differ and they can be combined.
What are like terms?
Like terms share the same variable part. The terms 6x and 11x are like terms. So are 3y2 and -8y2. But 5x and 5y are unlike, and so are 4x and 4x2.
How do you combine them?
Add or subtract the coefficients and keep the variable part. For 9a + 4a, add 9 + 4 to get 13a. Constants are like terms with each other as well: 7 and -2 combine to 5.
What does a full simplification look like?
Simplify 8k + 5 – 3k + 12.
- Group the k terms: 8k – 3k = 5k.
- Group the constants: 5 + 12 = 17.
- Result: 5k + 17.
Why does it work?
Think of k as a kind of object. Eight apples minus three apples leaves five apples, but you cannot merge apples with oranges.
What is a common error?
Combining unlike terms, such as writing 5k + 17 = 22k. The k and the constant stay separate.
Example: 7n + 2 + 4n – 9 simplifies to 11n – 7.