Watch out
Missing one of the four products.
Scottish National 5 Mathematics
National 5 Maths Expanding brackets
Expand single, double and linear-by-quadratic brackets with positive and negative coefficients.
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
- Multiply every term in one factor by every term in the other.
- Be ready to work exactly without a calculator and show each mathematical step.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Expanding brackets is an assessed part of Scottish National 5 Mathematics in the algebra area. Expand single, double and linear-by-quadratic brackets with positive and negative coefficients.
Multiply every term in one factor by every term in the other.
Keep negative signs attached to their terms.
Collect like terms only after expanding.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Key formulae and rules
- a(bx + c) = abx + ac
- (ax + b)(cx + d) = acx² + (ad + bc)x + bd
Check
Expand, factorise or substitute back into the original expression to verify the result.
Exam tip
Keep equations aligned line by line so method marks remain visible, especially through sign and bracket changes.
Worked examples
Worked example 1
Expanding brackets worked example
Expand (2x − 3)(x + 4)
- 2x(x + 4) − 3(x + 4)
- 2x² + 8x − 3x − 12
Answer: 2x² + 5x − 12
Watch out
- Missing one of the four products.
- Losing the negative sign on the constant product.