Like terms have the same variable part
3x and 5x are like terms, so they combine into 8x.
The x stays because both terms count the same kind of thing.
Year 7
Simplify linear expressions
Combine like terms accurately, explain why only matching terms can be collected, and spot equivalent expressions.
Lesson overview
Algebra - expressions and structure
An expression is a mathematical phrase made of terms. Terms with the same variable part are like terms, so they can be combined. Terms that do not match, such as x and y or x and a number, must stay separate. Simplifying means rewriting the expression so it is shorter but still has exactly the same value.
Constants combine with constants
In 4a + 3 + 2a + 5, the a terms combine and the numbers combine.
Keep variable terms and constant terms in clear groups.
Unlike terms stay separate
2x and 3y cannot be combined because the variable parts are different.
The expression is already simplified when no more like terms can be collected.
Worked example
Simplify 7p + 4 - 2p + 6.
| p terms | number terms |
|---|---|
| 7p and -2p | 4 and 6 |
| 5p | 10 |
- Group the like terms together: 7p - 2p and 4 + 6.
- Subtract the p terms to get 5p.
- Add the constants to get 10.
- Write the simplified expression as 5p + 10.
Try it
Collect like terms carefully and leave unlike terms separate.
Question 1
Which is the simplified form of 3x + 5x?
Question 2
Which is the simplified form of 4a + 3 - 2a?
Question 3
Which is the simplified form of 5m + 2n + 3m?
Question 4
Which statement is correct?
| x terms | constant |
|---|---|
| 2x and 4x | 1 |
Question 5
Which expression is already simplified?
different variables
like terms
like terms
Common mistakes
Watch for these when working through the lesson.
- Combining unlike terms, such as saying 2x + 3 equals 5x.
- Forgetting the sign in front of a term when collecting it.
- Dropping the variable when adding coefficients.
Related topics
These ideas fit closely with this lesson.
- Substitute into formulae.
- Generate and explain sequences.
- Mental and written arithmetic with integers, decimals and fractions.