Collecting Like Terms
Simplify algebraic expressions by collecting like terms — combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence
What a learner can do afterwards
- Identify like terms in an algebraic expression
- Combine like terms involving positive and negative coefficients
- Simplify expressions involving multiple variables and constant terms
The lesson
An expression can have several terms, like 3a + 2b + 5a. Some of these terms are like terms: they have the exact same variable raised to the same power. Only the coefficient, the number in front, can be different. 3a and 5a are like terms. 3a and 2b are not, because the letters are different.
Look at 3a + 2b + 5a. The terms 3a and 5a are like terms, so add their coefficients: 3 + 5 = 8. That gives 8a. The 2b has no partner, so it stays the same. The simplified expression is 8a + 2b.
Collecting works the same way with negative coefficients. In 7m - 2m + 4, the terms 7m and -2m are like terms: 7 + (-2) = 5, so you get 5m. The 4 is a constant with no matching term, so the answer is 5m + 4.
Only combine terms that match exactly: same letter, same power. Never fold a constant into a term that has a letter, and never multiply the letters together when you collect terms.
Collecting like terms means adding or subtracting the coefficients of terms that share the same variable and power, and leaving everything else untouched.
Watch it
Where it sits
Learn first
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.