Like Terms and Simplifying
Only terms with identical variable parts can be combined.
About this topic
Like terms have exactly the same variable parts, such as 3x and 5x, or 2y² and −7y². Only like terms can be combined, by adding or subtracting their coefficients: 3x + 5x = 8x. Unlike terms such as 3x and 3x² must stay separate.
Simplifying an expression means collecting like terms to write it as compactly as possible. This makes later steps easier, whether you are solving an equation, multiplying polynomials or checking whether two expressions are equal. Take 4x + 3y − 2x + 7y + 5. Group x terms (4x − 2x = 2x), y terms (3y + 7y = 10y) and the constant 5, giving 2x + 10y + 5.
Think of fruit: 3 apples plus 5 apples makes 8 apples, but 3 apples plus 5 oranges is just 3 apples and 5 oranges. Algebra works the same way, where the variable is the type of fruit. A coefficient of 1 is not written, so x means 1x, and a subtracted term carries its negative sign with it.
A common error is combining 3x and 4y into 7xy, or 2x and 3x² into 5x³. Those are unlike. Another is losing a sign when moving terms. A helpful habit is to circle or underline each type of term with a different mark before combining. Simplified expressions are also easier to evaluate and graph.
Key ideas
- 3x and 5x are like terms
- Add coefficients only
- x and x² are not like terms
Quick check
Use cases: where Like Terms and Simplifying helps
- Homework: review the key idea behind Like Terms and Simplifying before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Like Terms and Simplifying without notes.
- Visual learning: play with the interactive lab to see how Like Terms and Simplifying changes when you adjust its inputs.
- Teaching a friend: explain Like Terms and Simplifying in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Like Terms and Simplifying?
Only terms with identical variable parts can be combined.
What will I learn in Like Terms and Simplifying?
3x and 5x are like terms. Add coefficients only. x and x² are not like terms.
Is Like Terms and Simplifying part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Like Terms and Simplifying lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Like Terms and Simplifying?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.