Expanding single brackets

Tier: #Foundation #Higher

🔗What you need to know first

Simplifying expressions

How to

Multiplying terms within a bracket by the term in front. This process is the reverse of Basic factorising

e.g. $3(x+2)=3x+6$

You multiply everything inside the brackets by the term in front of the brackets. In the above case, $x$ is multiplied by 3 as is 2.

$2x(3x-4)=6x^2-8x$

Students often get caught out if there is a minus sign in front:

$-3(x-4)=-3x+12$

Especially if it's in the middle of an expression:

$2(x+3)-4(x-5)=2x+6-4x+20$

The final '+20' is missed a significant number of times!

Common topics that go alongside

Manipulating algebraic fractions

❓Questions to practise

Practise these questions →

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📝Past paper questions

2025 Jun 2H GCSE Q9 (1 mark)

2023 Nov 2H GCSE Q1 (2 marks)

2023 Jun 3H GCSE Q1 (2 marks)

2022 Jun 2H GCSE Q1 (2 marks)

2021 Nov 1H GCSE Q11 (2 marks)

2019 Jun 3H GCSE Q18 (1 mark)

2018 Jun 1H GCSE Q15 (1 mark)

2018 Jun 3H GCSE Q2 (1 mark)

2017 Nov 2H GCSE Q1 (1 mark)

2017 Jun 2H GCSE Q11 (1 mark)

💬What the examiners say

"Most students scored full marks. However, a significant number of students gave the correct answer in the working space but then misguidedly tried to "simplify" the expression by combining the two terms."

⬆️How you can quickly improve

Apply the index law explicitly when multiplying: xᵃ × xᵇ = x^(a+b), including when one of the indices is negative.
After expanding, check whether the remaining terms are genuinely like terms before combining — only group terms with the same variable and power.
Multiply every term inside the bracket by the factor outside, and check the sign of each product individually.

💡Watch

🔓What this unlocks

Expanding quadratics

ℹ️Calculator tricks