Why do we learn the method for binomial expansions if calculators are allowed?

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RevisionRosie04
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Surely just typing '(x-2)^10' into a calculator is easier? All our exams, calculators are allowed. So why do we need to learn it?
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Pyruvic Acid
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You can type that into a calculator that’s approved by the exam board?
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RevisionRosie04
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(Original post by Pyruvic Acid)
You can type that into a calculator that’s approved by the exam board?
Casio fx-991ES
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Joshwoods01
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it is used later on at university, we use it a lot for probabilities since that form follows the binomial distribution
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RevisionRosie04
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(Original post by Joshwoods01)
it is used later on at university, we use it a lot for probabilities since that form follows the binomial distribution
ok, thank you
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Joshwoods01
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additionally, calculators don't expand algebraic brackets (unless you have set the variable to a specific value) hence you use Pascals triangle to find the coefficients of the variable when it is expanded (if you've covered that yet)
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_gcx
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It is commonly used as part of a wider algebraic manipulation, sometimes to give a bound/estimate. You're right that the whole "find an approximation for blah^bleh by finding such and such expansion" is pointless.

To give an example, as mentioned above it has applications in probability and combinatorics. For example, setting x = 1 in the binomial theorem reveals that there are 2^n ways to take a sample from n objects. (https://proofwiki.org/wiki/Cardinali...te_Set/Proof_2) Some other examples on proofwiki: https://proofwiki.org/wiki/Special:W...Integral_Index.

If you are not already familiar, \binom n k is the number of ways to choose k objects from a collection of n distinct objects, which you can imagine pops up quite a bit. (so the number of ways to sample from n objects is (number of ways to choose 0 objects from the n) + (number of ways to choose 1 object from the n) + ... = \sum_{k = 0}^n \binom n k = 2^n)
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Joshwoods01
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(Original post by _gcx)
It is commonly used as part of a wider algebraic manipulation, sometimes to give a bound/estimate. You're right that the whole "find an approximation for blah^bleh by finding such and such expansion" is pointless.

To give an example, as mentioned above it has applications in probability and combinatorics. For example, setting x = 1 in the binomial theorem reveals that there are 2^n ways to take a sample from n objects. (https://proofwiki.org/wiki/Cardinali...te_Set/Proof_2) Some other examples on proofwiki: https://proofwiki.org/wiki/Special:W...Integral_Index.
we covered this at uni, quite an interesting concept I think
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_gcx
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For the bounding bit, I remember a question at uni that required basically pulling out the fact:

\displaystyle \frac 1 {(1 + \frac 1 n)^{n^2}} \le \frac 1 {1 + \frac {n^2} n + \frac {n^2(n^2 - 1)} {2 n^2}} = \frac 2 {1 + 2n + n^2}

It kind of just "comes up" like that.
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Aloe Striata
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(Original post by RevisionRosie04)
Surely just typing '(x-2)^10' into a calculator is easier? All our exams, calculators are allowed. So why do we need to learn it?
If you're in school/sixth form, you can't use a calculator that allows algebraic manipulation. you just can't. don't try it, you'll get disqualified if you write the exam using such a calculator. if you're in uni, then I don't know, if the calculator is allowed you should be able to do it on the calculator.
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RevisionRosie04
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I didn't want to go to uni but it sounds kind of fun now
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Qxi.xli
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(Original post by RevisionRosie04)
Surely just typing '(x-2)^10' into a calculator is easier? All our exams, calculators are allowed. So why do we need to learn it?
my calc doesn't do that wth it cost like 100 lol
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.Dezer.
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(Original post by Qxi.xli)
my calc doesn't do that wth it cost like 100 lol
broke gang :dance:
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RevisionRosie04
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(Original post by Qxi.xli)
my calc doesn't do that wth it cost like 100 lol
we've been doing online classes so I've just been using symbolab, rather than getting the calculator out of my bag, and assumed our school calculators work the same
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