The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

C2 Binomial Expansion

Hi everyone,

I'm hoping you can help me with a certain style of C2 Binomial Expansion.

I would like to know how to solve -

(a+bx)p(a+bx)^p

When you have values for a & b, and a coefficient of a term in the expansion but you need to find the value of p.

What would be the procedure of doing this?

Thanks - Andy.
(edited 13 years ago)
Need more info.
Reply 2
Avatar for Wilko94
Wilko94
OP
6
Original post by Circadian_Rhythm
Need more info.


Sorry - I forgot something - you know the coefficient of a term in the expansion also.
Reply 3
Avatar for .Stubert.
.Stubert.
Well, what would you do if you had P and needed to find the coefficient. Just do the same and you should get an equation you can solve.
Reply 4
Avatar for MinpoloD
MinpoloD
6
hey there
I believe you can do this by expanding it and then equating the two coefficients

Coefficient of x^2 in (1−2x)p=40 (1-2x)^p = 40
where P is greater than 0
So expanding to find x^2


\dbinom{P}{2}(1)^{P-2}(-2x)^2

I personally prefer the NCr formula but i can't seem to get it on latex.
Anyway
1^{p-2} = 1

So
\dbinom{P}{2}(-2)^2= 40

finding the value of \dbinom{P}{2} = \frac{P!}{(P-2)!2!}

= \dfrac{P(P-1)(P-2)!}{(P-2)!2!}
(P-2)! cancel out
So you are left with
\dfrac{P(P-1)}{2}
\dfrac{P^2-P}{2}

so going back to \dbinom{P}{2}(-2)^2= 40
We now can get to
4(\dfrac{P^2-P}{2})=40


I'm pretty sure you can solve the rest yourself. Good luck!

For future reference and cause i'm lazy this was Question 4 Exercise 5D of the C2 edexcel book

And apologies if this counts as a full solution, I aimed to do it as an example to the OP to show the method and did not go all the way to finding the answer
Reply 5
Avatar for Hoody93
Hoody93
1
The coefficient of which term, it's simply working backwards. Is it the a^2 term? etc?
Original post by MinpoloD
hey there
I believe you can do this by expanding it and then equating the two coefficients

Coefficient of x^2
in (1−2x)p=40 (1-2x)^p = 40
where P is greater than 0
So expanding to find x^2


\dbinom{P}{2}(1)^{P-2}(-2x)^2

I personally prefer the NCr formula but i can't seem to get it on latex.
Anyway
1^{p-2} = 1

So
\dbinom{P}{2}(-2)^2= 40

finding the value of \dbinom{P}{2} = \frac{P!}{(P-2)!2!}

= \dfrac{P(P-1)(P-2)!}{(P-2)!2!}
(P-2)! cancel out
So you are left with
\dfrac{P(P-1)}{2}
\dfrac{P^2-P}{2}

so going back to \dbinom{P}{2}(-2)^2= 40
We now can get to
4(\dfrac{P^2-P}{2})=40


I'm pretty sure you can solve the rest yourself. Good luck!

For future reference and cause i'm lazy this was Question 4 Exercise 5D of the C2 edexcel book

And apologies if this counts as a full solution, I aimed to do it as an example to the OP to show the method and did not go all the way to finding the answer

I think you made it too complicated when you could have just used n(n-1) /1x2 x^2 formula and from there its easier but i do see ur point
Reply 7
Avatar for MinpoloD
MinpoloD
6
Original post by Education_1
I think you made it too complicated when you could have just used n(n-1) /1x2 x^2 formula and from there its easier but i do see ur point


why reply to a thread which is over 6 months old just to to tell me my method is too complicated?
Original post by MinpoloD
why reply to a thread which is over 6 months old just to to tell me my method is too complicated?


Sorry MinpoloD i didnt realised that this thread was over 6 months (I'm kinda getting used to student room).. no dont minunderstand me I was just saying for the benefit of other people who is seeing this because my teacher didnt actually explain anything .. >< anyway your post of helpful I must admit because I was stuck on some question and I saw your reply.. thank you for explaining .. I didnt mean to offend

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you