Like terms combine because they count the same thing
3x and 4x are both x terms, so together they make 7x.
Keep the variable and add the coefficients.
Year 8
Simplify expressions review
Revisit Year 7 simplification by collecting like terms accurately, keeping signs correct, and preparing securely for brackets and equations.
Lesson overview
Algebra - Year 7 bridge and expression structure
Before expanding brackets or solving equations, it helps to be fully secure with simplifying expressions. Like terms have the same variable part, so they can be collected together. Constants combine with constants. Unlike terms must stay separate. This is Year 7 knowledge, but it remains useful throughout Year 8 algebra because it helps us see structure clearly.
Constants combine with constants
In 2a + 5 + 3a + 1, collect the a terms and the number terms separately.
| a terms | number terms | simplified |
|---|---|---|
| 2a and 3a | 5 and 1 | 5a + 6 |
Group by type before you combine.
Signs matter when collecting terms
In 6p - 2p + 3, the negative sign stays with 2p when you collect it.
Treat subtract 2p as negative 2p.
Worked example
Simplify 5x + 3 + 2x - 4.
| x terms | number terms | result |
|---|---|---|
| 5x and 2x | 3 and -4 | 7x - 1 |
- Group the like terms: 5x + 2x and 3 - 4.
- Add the x terms to get 7x.
- Combine the constants to get -1.
- Write the simplified expression as 7x - 1.
Try it
Collect matching terms carefully, and watch every sign before you combine.
Question 1
Simplify 4x + 3x.
Question 2
Simplify 6a + 2 - 4a.
Question 3
Simplify 5m + 2n + 3m.
| m terms | n terms |
|---|---|
| 5m and 3m | 2n |
Question 4
Simplify 9p - 5p + 4.
Question 5
Which expression is already simplified?
unlike terms
like terms
like terms
Common mistakes
Watch for these when working through the lesson.
- Combining unlike terms such as 2x + 3 into 5x.
- Forgetting that a subtraction sign changes the sign of the term after it.
- Dropping the variable when adding coefficients.
Related topics
These ideas fit closely with this lesson.
- Expand single brackets.
- Solve two-step linear equations.
- Substitute into formulae.