Multiply the outside term by each part
In 3(x + 4), the 3 multiplies x and it also multiplies 4.
| Expression | Partial products | Expanded form |
|---|---|---|
| 3(x + 4) | 3x and 12 | 3x + 12 |
Do not multiply only the first term inside the bracket.
Year 8
Expand single brackets
Expand a single bracket accurately, connect area structure to algebra, and explain why each term inside the bracket must be multiplied.
Lesson overview
Algebra - expressions and distributive structure
Expanding a single bracket means multiplying the term outside the bracket by every term inside it. This is the distributive structure of algebra. A quick area model can help because one side length is split into parts, so the full area is the sum of the smaller rectangles. The key is that every inside term is affected by the outside multiplier.
Area structure shows why expansion works
A rectangle with height 5 and width (x + 2) has two smaller areas.
so 5x + 10
The whole area equals the sum of the smaller parts.
Subtraction inside the bracket still affects both terms
In 4(y - 3), the 4 multiplies y and it multiplies negative 3.
Keep the sign with the second term when you multiply.
Worked example
Expand 6(a + 5).
| Outside term | Inside terms | Expanded form |
|---|---|---|
| 6 | a and 5 | 6a + 30 |
- Identify the factor outside the bracket: 6.
- Multiply 6 by a to get 6a.
- Multiply 6 by 5 to get 30.
- Write the expanded expression as 6a + 30.
Try it
Look for the outside factor first, then apply it to every term inside the bracket.
Question 1
Expand 2(x + 7).
Question 2
Expand 5(m + 3).
| 5 x m | 5 x 3 |
|---|---|
| 5m | 15 |
Question 3
Expand 4(y - 2).
Question 4
A rectangle has height 3 and width (x + 6). Which expression gives its area?
Question 5
Which statement is correct when expanding a single bracket?
| Expression | Correct expansion |
|---|---|
| 3(x + 2) | 3x + 6 |
Common mistakes
Watch for these when working through the lesson.
- Multiplying only the first term inside the bracket.
- Losing the sign on the second term, especially when subtracting.
- Adding the outside factor to the inside terms instead of multiplying.
Related topics
These ideas fit closely with this lesson.
- Solve two-step linear equations.
- Plot and interpret linear graphs from y = mx + c.
- Substitute into formulae.