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Algebra · Foundation & Higher

Expanding single brackets

Expanding a single bracket means multiplying the term outside the bracket by every term inside. This removes the bracket and gives an equivalent expression.

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Key facts to remember

  • 1Multiply the term outside by each term inside the bracket.
  • 2Take care with negative signs: −3(2x − 5) = −6x + 15.
  • 3Expanding and simplifying may require collecting like terms afterwards.
  • 4The reverse of expanding is factorising.
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Worked examples

Example 1

Expand and simplify 4(3x + 2) − 2(x − 5)

Working

  1. Expand 4(3x + 2) = 12x + 8
  2. Expand −2(x − 5) = −2x + 10
  3. Collect like terms: 12x − 2x + 8 + 10
  4. = 10x + 18
Answer10x + 18
Example 2

Expand 3x(2x² − 5x + 1)

Working

  1. 3x × 2x² = 6x³
  2. 3x × (−5x) = −15x²
  3. 3x × 1 = 3x
  4. = 6x³ − 15x² + 3x
Answer6x³ − 15x² + 3x
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Common mistakes

✗Only multiplying the first term inside the bracket and forgetting subsequent terms.
✗Sign errors: −2(x − 5) becomes −2x − 10 instead of −2x + 10.
✗Forgetting to collect like terms after expanding multiple brackets.
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Exam tips

✓Draw arrows from the outside term to each inside term to ensure you multiply everything.
✓Be especially careful when the term outside is negative — a negative × negative = positive.

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