Multiple General Binomial Expansion (Edexcel A Level Maths) : Revision Note
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General Binomial Expansion - Multiple
What is the general binomial expansion?
The general binomial expansion, as given in the formula booklet, is

If n ∈ ℕ then the expansion is finite (see Binomial Expansion)
Otherwise the expansion is infinitely long
It is only valid for |x| < 1 (-1 < x < 1)
Only the first few terms of an expansion are usually needed
What is meant by multiple general binomial expansions?
More than one part of an expression can be a binomial expansion
These may sometimes be called compound expressions
The expansion will only be valid for the lowest |x| boundary from all the expansions used
How do I use general binomial expansions in complicated expressions?
STEP 1 Break the expression down into binomial expansions
STEP 2 Expand each binomial individually, up to a suitable number of terms
Be careful with negatives and fractions
Use brackets as appropriate
STEP 3 Collect the expansions together and simplify
This could be expanding brackets, collecting like terms, etc
Ignore any terms of degree higher than required
STEP 4 Check the validity of each binomial expansion
The overall validity is the intersection (∩)

How do I work with partial fractions and the general binomial expansion?
Partial fractions allow rational expressions to be written in a form where the general binomial expansion can then be applied
Validity is an important part of the general binomial expansion

Worked Example


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