Expanding double brackets - easier
Expanding double brackets helps you work out the full expression when two binomials are multiplied together, which is useful in algebra, area problems, and later topics like quadratic equations. It gives you a quick way to simplify expressions and spot patterns that appear throughout maths. Jump to the questions
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Worksheet preview and key skills
Worksheet preview
Practise expanding double 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 in the first bracket by each term in the second bracket.
- Expanding double brackets systematically.
- Collecting like terms.
- Writing the final expanded expression.
Use the interactive worksheet below, or read the Topic guide for the method and worked example.
Topic guide
What this worksheet practises
This worksheet focuses on expanding double brackets, such as (x + 3)(x + 5). This is a foundational algebraic skill used to turn factorised expressions into quadratic expressions.
Key method
To expand double brackets, you must multiply every term in the first bracket by every term in the second bracket. Many people remember this using the FOIL method:
- Firsts: Multiply the first terms of each bracket.
- Outsides: Multiply the outer terms of the two brackets.
- Insides: Multiply the inner terms of the two brackets.
- Lasts: Multiply the last terms of each bracket.
After multiplying, write out all four terms in a line. Finally, simplify your answer by collecting any like terms (usually the middle two x terms).
Worked example
Expand and simplify: (2x + 1)(x + 4).
Step 1: Firsts. Multiply 2x by x = 2x².
Step 2: Outsides. Multiply 2x by 4 = 8x.
Step 3: Insides. Multiply 1 by x = 1x (or simply x).
Step 4: Lasts. Multiply 1 by 4 = 4.
Step 5: Write out the full expression: 2x² + 8x + x + 4.
Step 6: Simplify by collecting the like terms (8x + x = 9x).
The final answer is 2x² + 9x + 4.
Common mistakes to avoid
A frequent error is only multiplying the first terms and the last terms, for instance thinking that (x + 3)(x + 5) becomes x² + 15. You must remember the "Outsides" and "Insides" to generate the middle terms.