GCSE MATHS • FOUNDATION & HIGHER
Expanding Brackets Made Simple
Learn how to multiply every term correctly, handle negative signs and expand single and double brackets using a clear step-by-step method.
Clear method
Exam practice
Worked proofs
Proof in Four Moves
1
Identify
Find the factor outside the bracket and every term inside the bracket.
2
Multiply
Multiply the outside factor by each term inside, including its sign.
3
Remove
Write the products without the bracket.
4
Simplify
Collect like terms if the expanded expression contains any.
What You’ll Learn
Expand Single Brackets
Multiply a numerical or algebraic factor by every term inside one bracket.
Manage Negative Signs
Apply sign rules accurately when the outside factor or an inside term is negative.
Simplify After Expanding
Collect like terms once the brackets have been removed.
Expand Double Brackets
Multiply every term in the first bracket by every term in the second bracket.
Key Representations
Distributive Rule
a(b + c) = ab + ac
Subtraction Inside a Bracket
a(b − c) = ab − ac
Negative Outside Factor
−a(b + c) = −ab − ac
Double Brackets
(a + b)(c + d) = ac + ad + bc + bd
Worked Proof: Consecutive Numbers
1.Identify
The factor outside the bracket is 2. The terms inside are x and +3.
2. Multiply Every Term
2 × x = 2x and 2 × 3 = 6
3. Remove the Brackets
2x + 6 + x
4. Write the Final Answer
3x + 6
More Worked Examples
1
Positive Single Bracket
3(x + 4)
2. Multiply 3 by 4 to get 12.
2
Subtraction Inside a Bracket
5(x − 2)
2. Multiply 5 by −2 to get −10.
3
Negative Outside Factor
−2(x − 5)
2. Multiply −2 by −5 to get +10.
4
Double Brackets
(x + 2)(x + 3)
2. Collect the like terms 3x and 2x.
- Common GCSE Mistakes
- Multiplying only the first term
- Losing a negative sign
- Adding instead of multiplying
- Missing products in double brackets
- Combining unlike terms
- Exam Tips
- Draw a multiplication arrow from the outside factor to every term inside a single bracket.
- Keep each positive or negative sign attached to its term throughout the expansion.
- For double brackets, write all four products before collecting like terms.
- Show the expansion step clearly; it makes sign errors easier to spot.
- Check that the brackets are removed and all resulting like terms are simplified.
Skills Used in Expanding Brackets
Ready to Practise?
Printable Worksheet
Practise single brackets, negative factors and double brackets using printable questions with answers.
Interactive Quiz
Test each multiplication step and receive instant feedback on signs and simplification.
Exam-Style Questions
Apply expansion skills to longer GCSE algebra questions.
Watch the Expanding Brackets Tutorial
Follow a clear step-by-step explanation of distributing a factor, managing negative signs, simplifying after expansion and multiplying double brackets.
Frequently Asked Questions
Expanding brackets means multiplying each term inside a bracket by the factor outside it, then writing the result without brackets. For example, 3(x + 4) = 3x + 12.
Multiply the negative number by every term inside and use the sign rules carefully. For example, −2(x − 5) = −2x + 10 because −2 × −5 = +10.
With double brackets, every term in the first bracket multiplies every term in the second. For (x + 2)(x + 3), the four products are x², 3x, 2x and 6 before the like terms are collected.
Expand the brackets first. Then collect any like terms in the resulting expression. For example, 2(x + 3) + x becomes 2x + 6 + x, then 3x + 6.
