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SQA National 5 Mathematics

Expanding double brackets

Multiplying two brackets and collecting like terms.

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

For expanding double 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.
  • Quadratic form: ax² + bx + c

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

Expand brackets

Expand (x + 2)(x + 5)

  1. First terms: x multiplied by x gives x²
  2. Outer and inner terms: 5x + 2x = 7x
  3. Number term: 2 × 5 = 10

Answer: x² + 7x + 10

Worked example 2

Factorise a quadratic

Factorise x² + 6x + 8

  1. Find two numbers that multiply to 8 and add to 6.
  2. The numbers are 2 and 4.

So: (x + 2)(x + 4).

Worked example 3

Solve from factors

Solve (x − 3)(x + 4) = 0.

  1. Set each bracket equal to zero.
  2. x − 3 = 0 or x + 4 = 0

Answer: x = 3 or x = −4

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.