Approximating Values using the Binomial Expansion (AQA A Level Maths) : Revision Note
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Approximating Values
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
How do I use a binomial expansion to approximate a value?

Ignoring higher powers of x leads to an approximation
The more terms the closer the approximation is to the true value
For most purposes, squared or cubed terms are accurate enough

STEP 1 Compare the value you are approximating to (a + bx)n
STEP 2 Solve the appropriate equation to find the value of x
STEP 3 Substitute this value of x into the expansion to find the approximation
Examiner Tips and Tricks
You can get a good idea if your approximation is correct by working out the “real” answer using your calculator.
Sometimes it helps to factorise out a number before approximating
Worked Example



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