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# Expanding single brackets - easier problems
- URL: https://www.esheets.io/expanding-single-brackets-easier-problems/
- Published: 2025-05-17T15:38:04.000Z
- Updated: 2026-06-21T16:42:06.000Z
- Author: Richard Linnington
- Tags: Maths, Algebra

You’ll often come across expressions like 3(x + 4) in algebra – and learning to expand single brackets helps you simplify these expressions. This skill pops up all over the place, from working out costs in real-life problems to solving equations in science and engineering. [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise expanding single brackets with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Multiplying each term inside the bracket.
- Applying the multiplier to every term.
- Handling positive and negative terms carefully.
- Writing the expanded expression.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

Expand the following expressions using the grid method.

  
## Topic guide

### What this worksheet practises

This worksheet provides practice on the fundamental skill of expanding single brackets. In algebra, a number or letter sitting directly outside a bracket means "multiply everything inside".

### Key method

To expand the bracket, you must distribute the outside term across every term inside.

- Identify the term immediately outside the bracket.
- Draw a small arrow pointing from the outside term to the **first** term inside. Multiply them together and write the result down.
- Draw a second arrow from the outside term to the **second** term inside. Multiply them together. Be careful with any negative signs.
- Combine these two results into a single algebraic expression.

### Worked example

**Expand 4(3x − 5).**

Step 1: Multiply the outside number (4) by the first term inside (3x).

4 × 3x = 12x.

Step 2: Multiply the outside number (4) by the second term inside (−5).

4 × −5 = −20.

Step 3: Write out the complete expression.

12x − 20.

### Common mistakes to avoid

The most common and frustrating mistake for examiners to see is a student multiplying the first term correctly but completely forgetting to multiply the second term. For example, expanding 4(3x − 5) to become 12x − 5\. You *must* multiply every single item inside the bracket by the number outside.

### How to check your answer

Pick a simple number, like x = 2\. Substitute it into the original question: 4 × (3(2) − 5) = 4 × (6 − 5) = 4 × 1 = 4\. Now substitute it into your answer: 12(2) − 20 = 24 − 20 = 4\. Because both calculations give the same result, your algebra is correct.