GCSE Maths → Algebra → Expanding Brackets
Expanding Brackets GCSE Maths: Step-by-Step Guide
Expanding brackets is one of the most important algebra skills in GCSE maths. It means removing brackets by multiplying carefully. This skill appears in simplifying expressions, solving equations, factorising, quadratics, graphs, and rearranging formulae.
Expanding brackets is also closely linked to factorising. Expanding removes brackets, while factorising puts brackets back in.
Video explanation
A short Worthing Maths Tutor video explanation for expanding brackets GCSE maths can be embedded here later to improve student engagement and time on page.
What does expanding brackets mean?
Expanding brackets means multiplying the term outside the bracket by every term inside the bracket.
The 3 must multiply both x and 4. A common mistake is to multiply only the x and forget the 4.
Method: expanding one bracket
- Look at the term outside the bracket.
- Multiply it by the first term inside the bracket.
- Multiply it by the second term inside the bracket.
- Keep the correct signs.
- Simplify if needed.
Example 1: Expand 5(a + 2)
Multiply 5 by both terms inside the bracket.
So:
Example 2: Expand 4(x - 7)
Multiply 4 by x and then multiply 4 by -7.
So:
Expanding brackets with negative numbers
Negative signs are one of the biggest reasons students lose marks in GCSE algebra. Take your time and multiply the signs carefully.
Example 3: Expand -3(y + 5)
Multiply -3 by y and then multiply -3 by 5.
So:
Example 4: Expand -2(x - 6)
This time the second term inside the bracket is negative.
So:
Expanding when there is more than one term outside
Example 5: Expand 3(2x + 5)
Multiply 3 by both terms inside the bracket.
So:
Example 6: Expand 4(3y - 2)
So:
Expanding two brackets
At GCSE Higher level, students often need to expand two brackets. This means every term in the first bracket must multiply every term in the second bracket.
Example 7: Expand (x + 2)(x + 5)
Multiply each pair of terms:
Now collect like terms:
Example 8: Expand (x - 3)(x + 4)
Multiply each term carefully:
Collect like terms:
Common mistakes in expanding brackets
- Forgetting to multiply every term inside the bracket.
- Writing 3(x + 4) as 3x + 4 instead of 3x + 12.
- Making sign mistakes with negative numbers.
- Expanding two brackets but missing one multiplication.
- Forgetting to collect like terms at the end.
Practice questions
Try these questions before checking the answers.
- Expand 2(x + 6)
- Expand 7(a - 3)
- Expand -4(y + 8)
- Expand -5(x - 2)
- Expand 3(2x + 5)
- Expand 4(3y - 2)
- Expand (x + 3)(x + 4)
- Expand (x - 2)(x + 5)
Answers
- 2x + 12
- 7a - 21
- -4y - 32
- -5x + 10
- 6x + 15
- 12y - 8
- x² + 7x + 12
- x² + 3x - 10
Expanding brackets FAQ
What does expanding brackets mean?
Expanding brackets means removing brackets by multiplying the term outside the bracket by every term inside the bracket.
What is the most common mistake when expanding brackets?
The most common mistake is multiplying only the first term inside the bracket and forgetting to multiply the second term.
How do you check expanding brackets?
You can check by seeing whether every term inside the bracket has been multiplied by the outside term, and by simplifying any like terms correctly.
Is expanding brackets important for GCSE maths?
Yes. Expanding brackets is used in simplifying expressions, solving equations, factorising, quadratics, graphs, and rearranging formulae.
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