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General Binomial Expansion - Subtleties (CIE A Level Maths: Pure 3)
Revision Note
General Binomial Expansion - Subtleties
What is the general binomial expansion?
- The binomial expansion applies for positive integers, n ∈ ℕ
- The general binomial expansion applies to other types of powers too
- The general binomial expansion applies for all real numbers, n ∈ℝ
- 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
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- 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
Worked example
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