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# Explain the binomial therom watch

1. ok i ALWAYS seem to get binomial questions wrong. I have read it over in my book and just don see where I am going wrong, see my other thread if you want an example.
http://www.thestudentroom.co.uk/t123586.html
So can someone please just give me a brief outline of how to do binomial expansions I will be really greatful, and rep the person/people that help the most. thank you
2. There are two formulas used for binomial expansion, it depends which module you are doing. For C2 its the one with ! and for C4 it's a different one. Which are you doing?
3. I am doing p2. the one in my book is where you use ncr n!/r!(n-r!) although in the p2 paper they seem to do something else.
4. This page does a good job of explaining it I think:
http://www.mathsrevision.net/alevel/pages.php?page=3
5. (Original post by JohnC)
http://www.mathsrevision.net/alevel/pages.php?page=3
thatnks but that just explains the formula i already know that doesn't seem to work when applied to questions i hate alevels
6. One thing that really helps me is if I put brackets around every calculation and don't try to do anything in my head without writing it down first. Usually I get it wrong because of things like wrong negative signs or something so doing that really helps. Do you just keep making small mistakes or do you always get it totally wrong?
7. (Original post by fabz)
One thing that really helps me is if I put brackets around every calculation and don't try to do anything in my head without writing it down first. Usually I get it wrong because of things like wrong negative signs or something so doing that really helps. Do you just keep making small mistakes or do you always get it totally wrong?
totally wrong, I seem to have ! everywhere where the mark scheme doesnt, and different expressions.
8. Do you have a calculator with the nCr button???
9. yea I do but some questions require it to be done with algebra, sorry to keep going on about it but exactly like in the linked post, so you can't use that
10. Sorry I've been so useless, P2 sucks. All you have to do in C2 is number crunch.
11. (Original post by fabz)
Sorry I've been so useless, P2 sucks. All you have to do in C2 is number crunch.
Hey, you havn't been useless at all, you are trying to help

I have seen some bizarre log qs from c2 so I don't envy u you at all

12. Thanks! Luck back at you!
13. (Original post by fabz)
Thanks! Luck back at you!
cheerz chica
cheerz chica
I don't see what is difficult about the binomial expansions, rather then the fact that you need to practise it more, sure you'll get some questions wrong, but keep going!

First thing in a binomial question, there will ONLY be two terms in the bracket and the whole expression will be powered by a variable n.

so : ( t + cx ) ^ n

where t and c are constants and x is the variable and n is the power to which the expansion is to be evaluted to.
usually c would be 1, so...

( t + x ) ^ n

lets take an example...

( 1 + x )²
this is the same as (1+x)(1+x) expanding this you get 1+2x+x², sort in ascending powers:
x²+2x+1

Using the binomial you would do the following calculation:

(2C0)(1)²(x)^0 + (2C1)(1)^1(x)^1 + (2C2)(1)^2(x²)
This would give: 1² + 2x + (1)x²
simplify and re-arrange: x² + 2x + 1

this is the same as how we expanded the above, to end up with the same three terms!

If the terms are such that:

( t - cx )^n

As there is a negative, treat it as part of the term cx, so (-cx)
15. what i am asking is why and how would nc2 when n>2 become n(n-1)/2 and not n!/2!(n-2)!
16. given n!/2!(n-2)!, we are cancelling all the factors common to n! and (n-2)!...which is the entire of (n-2)! and this leaves simply n(n-1) on the top.

the n(n-1)/2! expression is also valid for all rationals, whereas nC2 is only valid for integers where n>=2.
what i am asking is why and how would nc2 when n>2 become n(n-1)/2 and not n!/2!(n-2)!
Ok, its a matter of cancellation, in the P2 or C2 exam, your not allowed a calculator, so fair enough you have to memorise the formula:

n!/r!(n-r)! for nCr.

Now you can't do large expansions using this formula without a calculator!

n! / 2!(n-2)!

if you expand this:

n x (n-1) x (n-2) x (n-3) ....
2 x (n-2) x (n-3) x (n-4) x (n-5) .....

notice that (n-2) on the numerator will cancel with (n-2) on denominator and also (n-3) and (n-4) all the way until it stops!
to get:

n x (n-1)
2

This is your n(n-1) / 2

I hope thats cleared things up.

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