General Binomial Expansion - Subtleties (CIE A Level Maths: Pure 3)

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General Binomial Expansion - Subtleties

What is the general binomial expansion?

  • The binomial expansion applies for positive integers, n
  • The general binomial expansion applies to other types of powers too

 GBE Subtleties Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

 

  • The general binomial expansion applies for all real numbers,
  • Usually fractional and/or negative values of n are used
  • It is derived from (a + b)n, with a = 1 and b = x
  • Even when a ≠ 1 the general binomial expansion can still be used

How do I use the general binomial expansion for (a + kx)n?

The general binomial expansion can be applied to expanding (a + kx)n

STEP 1        Rewrite the question into (1 + bx)n form

    • Roots are fractional powers
    • Denominators are negative powers
    • A factor may be needed to make “a = 1

STEP 2        Replace “x” by “bx” in the expansion

Check carefully to see if b is negative

STEP 3        Expand and simplify

Use a line for each term to make things easier to read and follow

Use brackets

STEP 4        If required, check and state the validity statement, |bx| < 1

GBE Subtleties Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

Worked example

GBE Subtleties Example Diagram 1, A Level & AS Level Pure Maths Revision Notes

GBE Subtleties Example Diagram 2

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.