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# Expanding three brackets
- URL: https://www.esheets.io/expanding-three-brackets/
- Published: 2025-01-12T11:47:56.000Z
- Updated: 2026-06-21T16:42:07.000Z
- Author: Richard Linnington
- Tags: Maths, Algebra

Expanding triple brackets is a key skill in algebra that helps us simplify complex expressions. This technique is often used in areas like physics and engineering to model real-world scenarios, such as calculating the volume of irregular shapes or solving equations involving multiple variables. [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise expanding three 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

- Expanding two brackets first.
- Multiplying the result by the third bracket.
- Collecting like terms.
- Writing the final expanded expression.

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

Each question can be expanded into the form: ax³ + bx² + cx + d

Find the values of a, b, c and d

  
## Topic guide

### What this worksheet practises

This worksheet focuses on expanding three brackets multiplied together, such as (x+1)(x+2)(x+3). This is a higher-level algebraic skill that results in a cubic expression (containing x³). It requires careful organisation and systematic working to avoid losing terms.

### Key method

You cannot expand three brackets all at once. You must break the problem down into two manageable stages.

- Ignore the first bracket entirely for a moment.
- Expand the *second and third* brackets using the standard FOIL method.
- Simplify this result by collecting the like terms (the 'x' terms in the middle). Put large brackets around this new quadratic expression.
- Bring down the first bracket you ignored earlier.
- Now, multiply the two terms in your first bracket by the three terms in your new large bracket. This will create six separate terms.
- Collect all the like terms (x³, x², x, and numbers) to find your final cubic expression.

### Worked example

**Expand and simplify (x + 2)(x + 3)(x + 4).**

Step 1: Expand the last two brackets: (x + 3)(x + 4).

x² + 4x + 3x + 12 = x² + 7x + 12.

Step 2: Bring down the first bracket to multiply against this new expression.

(x + 2)(x² + 7x + 12).

Step 3: Multiply 'x' by everything in the second bracket.

x³ + 7x² + 12x.

Step 4: Multiply '2' by everything in the second bracket.

\+ 2x² + 14x + 24.

Step 5: Write it all out and collect like terms.

x³ + (7x² + 2x²) + (12x + 14x) + 24

The final answer is x³ + 9x² + 26x + 24.

### Common mistakes to avoid

A disastrous mistake is trying to multiply the 'x's together and the numbers together, arriving at an answer like x³ + 24\. This skips all the cross-multiplication. You must methodically multiply every term by every other term across the brackets.

### Things to remember

If you see a question written as (x + 5)³, do not panic. This simply means (x + 5)(x + 5)(x + 5). Write it out in full immediately, and then apply the exact same two-stage method described above.