National 5 Maths
Expanding Brackets
Course content
- Expanding algebraic expressions of these four types:
- \(a(bx+c)+d(ex+f)\)
- \(ax(bx+c)\)
- \((ax+b)(cx+d)\)
- \((ax+b)(cx^2+dx+e)\)
Integer
The set of integers is the set of whole numbers {0,1,2,3,...} together with their negative counterparts {-1,-2,-3,...}.
Key ideas
- For types 3 and 4 above, each term in the first bracket is multiplied by each term in the second bracket.
- Take care with \(+\) and \(-\) signs:
- positive \(\times\) negative \(=\) negative
- negative \(\times\) negative \(=\) positive
- We should always collect like terms to simplify our answers fully.
Textbook page references
- TeeJay Maths Book N5 pp.13-17
- Zeta National 5+ Maths pp.27-36
- Leckie National 5 Maths pp.27-34
Self-study course
- National5.com Highly recommended. Save £10 with discount code 'Maths.scot'.
Example 1 (Type 1)
Multiply out the brackets and collect like terms: \(5(x+4)+3(2x+1)\)
Example 2 (Type 1)
Multiply out the brackets and collect like terms: \(-2(3x+4)+5(2x-5)\)
Example 3 (Type 2)
Expand \(x(3x + 4)\)
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Example 4 (Type 2)
Expand \(6x(-2x + 3)\)
Example 5 (Type 3)
Expand the brackets and collect like terms: \((x+2)(x+5)\)
Example 6 (Type 3)
Expand the brackets and collect like terms: \((-x+6)(3x-5)\)
Recommended student books
Zeta Maths: National 5+ practice bookLeckie: National 5 Maths textbook
Example 7 (Type 4)
Expand and simplify fully: \((x+2)(x^2+x+3)\)
Example 8 (Type 4)
Expand and simplify fully: \((2x-1)(7x^2+x-5)\)
Example 9 (non-calculator)
SQA National 5 Maths 2014 P1 Q2
Expand the brackets and collect like terms: \((2x-5)(3x+1)\)
Recommended revision guides
How to Pass National 5 MathsBrightRED N5 Maths Study Guide
Example 10 (non-calculator)
SQA National 5 Maths 2015 P1 Q4
Multiply out the brackets and collect like terms: \((x-4)(x^2+x-2)\)
Example 11 (non-calculator)
SQA National 5 Maths 2017 P1 Q4
Expand and simplify \((2x+3)(x^2-4x+1)\)
Example 12 (non-calculator)
SQA National 5 Maths 2018 P1 Q4
Expand and simplify \((3x+1)(x-1)+2(x^2-5)\)
N5 Maths practice papers
Non-calculator papers and solutionsCalculator papers and solutions
Example 13 (non-calculator)
SQA National 5 Maths 2019 P1 Q3
Expand and simplify \((x+5)(2x^2-7x-3)\)
Example 14 (non-calculator)
SQA National 5 Maths 2023 P1 Q2
Expand and simplify \((x+7)^2+6(x^2-10)\)
Example 15 (non-calculator)
SQA National 5 Maths 2024 P1 Q3
Expand and simplify \((x+1)(x^2-4x+5)\)
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Maths.scot worksheet
• Expanding brackets worksheet • Answer sheet • See all National 5 Maths worksheets |
Past paper questions
• All past paper questions by topic |
Routine expansion: • 2014 Paper 1 Q2 • 2015 Paper 1 Q4 • 2017 Paper 1 Q4 • 2018 Paper 1 Q2 • 2019 Paper 1 Q3 • 2021 Paper 1 Q3 • 2022 Paper 2 Q1 • 2023 Paper 1 Q2 • 2024 Paper 1 Q3 |
Within other topics: • 2013 Spec. P1 Q7 (with indices) • 2016 Paper 1 Q12 (with quadratics) • 2017 Spec. P2 Q16 (with quadratics) • 2024 Paper 1 Q13 (with indices) |
Other great resources
Video - Larbert High School |
Video - Tynecastle HS Includes expanding three brackets |
Video - LHS Maths |
Videos - Clelland Maths 1. Single brackets 2. Double brackets |
Video - DLB Maths SQA 2014 Paper 1 Q2 solution |
PowerPoint - MathsRevision.com |
Lesson notes - Maths 777 1. Expanding and simplifying 2. Pair of brackets: both linear 3. Linear times quadratic 4. Expanding brackets: all types |
Notes - BBC Bitesize Test yourself - BBC Bitesize |
Notes - National5.com |
Notes - MathCentre.ac.uk |
Essential Skills worksheets • Linear times linear (Answers) • Linear times quadratic (Answers) |
Practice questions - Maths Hunter |
Worksheet - St Andrew's Academy Exercise on page 6 |
Worksheet - Airdrie Academy |
Exercises - Larkhall Academy Pages 21-25 Ex 2-6 (no answers) |
Click here to study the expanding brackets notes on National5.com.
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