CIE AS Maths: Pure 1

Revision Notes

1.1.1 Expanding Brackets

Test Yourself

Expanding Quadratics

You should be familiar with all aspects of basic algebra including manipulating expressions; simplifying; expanding and factorising brackets with both linear and quadratics.  In Pure Mathematics it is important that you are confident working with quadratics.

How do we expand two brackets?

  • You will have learnt a method for expanding double brackets in previous courses
    • The quickest and most common method is to use FOIL
      • First term in each bracket
      • Outside terms
      • Inside terms
      • Last terms
    • For (ax + b)(cx + d) you will have acx2 + adx + bcx + bd
  • Once you have expanded and multiplied all four terms simplify the two middle terms to give you a three-term quadratic
    • acx2 + (ad + bc)x + bd
  • Take extra care when working with negatives
  • Look out for a linear expression squared, this must still be treated as double brackets
    • (ax + b)2 = a2x2 + 2abx + b2
  • Makes sure you can recognise when a problem involves the difference of two squares
    • (ax + b)(axb) = a2x2 + abx - abx - b2 = a2x2 - b2
    • Spotting this will be particularly useful in many areas of Pure Mathematics

What if there is a quadratic in one (or both) of the brackets?

  • Treat these the same as expanding double brackets with two linear expressions
  • Take care with powers, remember the laws of indices
  • Look carefully to see if the terms can be simplified or not
    • For (ax2 + b)(cx2 + d) you will have acx4 + adx2 + bcx2 + bd = acx4 + (ad + bc)x2 + bd
    • For (ax2 + b)(cx + d) you will have acx3 + adx2 + bcx + bd

Worked example

1-1-1-expanding-brackets-we-solution-1-1

Exam Tip

Be extra careful with negatives!

Further Expanding

What do I need to know about expanding brackets?

  • To expand brackets, the rule is that each term in one set of brackets must be multiplied by each term in the other set of brackets

2.5.1 Expanding Brackets Illustration, Edexcel A Level Maths: Pure revision notes 

  • 'FOIL' is a special case of this, when each set of brackets contains two terms
  • If you are trying to expand something like (a + b)n for powers of n greater than 2 or 3, use the binomial expansion
  • If you have to expand more than two sets of brackets, just expand them two at a time:

Worked example

2.5.1 Expanding Brackets Multiple, Edexcel A Level Maths: Pure revision notes

Worked example

2.5.1 Expanding Brackets Example, Edexcel A Level Maths: Pure revision notes

You've read 0 of your 0 free revision notes

Get unlimited access

to absolutely everything:

  • Downloadable PDFs
  • Unlimited Revision Notes
  • Topic Questions
  • Past Papers
  • Model Answers
  • Videos (Maths and Science)

Join the 80,663 Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Lucy

Author: Lucy

Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels. Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all. Lucy has created revision content for a variety of domestic and international Exam Boards including Edexcel, AQA, OCR, CIE and IB.