What is important to know about Expanding single brackets?

Multiply the term outside by each term inside the bracket.

What is important to know about Expanding single brackets?

Take care with negative signs: −3(2x − 5) = −6x + 15.

What is important to know about Expanding single brackets?

Expanding and simplifying may require collecting like terms afterwards.

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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

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

Answer10x + 18

Example 2

Expand 3x(2x² − 5x + 1)

Working

3x × 2x² = 6x³
3x × (−5x) = −15x²
3x × 1 = 3x
= 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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