Back to National 5 Mathematics

SQA National 5 Mathematics

Expanding brackets

Multiplying out single and double brackets correctly.

Formula referenceMixed revision

Formula reference

Check the National 5 rules and formulae linked to this topic.

Which method?

Match exam clues to a suitable method.

Before you start

  • Read the command word and identify what is being asked.
  • Write down the relevant formula, rule or algebraic structure before substituting values.
  • Keep working set out line by line so method marks are clear.
National 5 Mathematics lesson

Explanation

Expanding brackets is part of Number and Algebra in SQA National 5 Mathematics. The key skill is choosing a method and communicating the working clearly.

For expanding brackets, underline the values or algebraic terms you are given, choose the matching rule, then simplify one line at a time.

National 5 answers should show enough working for a marker to follow the method. Exact answers are expected where the question asks for exact form; otherwise round only at the end.

Key formulae and rules

  • Calculator and non-calculator methods may both be useful.

Watch out

Choosing a method from a remembered keyword instead of reading the whole question.

Check

Compare your answer with the size you expected from the question.

Exam tip

Method marks come from clear setup and correct mathematical notation, not just a final answer.

Calculator tip

Use brackets for fractions, powers and square roots, then round only at the final line.

Worked examples

Worked example 1

Simplify an expression

Simplify 3x + 4x − 2.

  1. Collect like terms: 3x + 4x = 7x
  2. Keep the constant term −2.

Answer: 7x − 2.

Worked example 2

Solve an equation

Solve 5x − 7 = 18.

  1. Add 7 to both sides: 5x = 25
  2. Divide by 5.

So: x = 5

Worked example 3

Check the answer

Check x = 5 in 5x − 7 = 18

  1. 5(5) − 7 = 25 − 7
  2. 25 − 7 = 18

Answer: The solution checks correctly.

Watch out

  • Choosing a method from a remembered keyword instead of reading the whole question.
  • Dropping negative signs, powers or brackets during the working.
  • Giving a rounded decimal when an exact answer or algebraic form is needed.