Binomial expansions - alternative formulae Q

Hi - very stuck as Ive tried a few ways to approach this question.

I've just been reading about alternative forms for binomial expansions.

I was taught....
(1+x)^n =

1 + nx + n(n-1)/2! * x^2 + n(n-1)(n-2)/3! *x^3


This is the question.

The first three terms in the expansion, in ascending powers of x, of (1+px)^n =

1 - 18x + 36p^2x^2.
Given that n is a positive integer, find the value of n and the value of p.



I could just do with a nudge!

Thanks

Hi - very stuck as Ive tried a few ways to approach this question.

I've just been reading about alternative forms for binomial expansions.

I was taught....
(1+x)^n =

1 + nx + n(n-1)/2! * x^2 + n(n-1)(n-2)/3! *x^3


This is the question.

The first three terms in the expansion, in ascending powers of x, of (1+px)^n =

1 - 18x + 36p^2x^2.
Given that n is a positive integer, find the value of n and the value of p.



I could just do with a nudge!

Thanks

Did you manage it?

Posted from TSR Mobile

No lol sorry

n(px) = 18x

n(n-1)/2 *px^2. = 36(px)^2

Where next?

Thanks

So np = 18

And n(n-1)/2 = 36

So np = 18

And n(n-1)/2 = 36

NP =-18 (he's missed the - sign not your mistake but will make the answer different)

Posted from TSR Mobile

NP =-18 (he's missed the - sign not your mistake but will make the answer different)

Posted from TSR Mobile

Thanks both got it.... I have another one. Tut. I will start another thread... Lol

Good point ... I have corrected my post

NP =-18 (he's missed the - sign not your mistake but will make the answer different)

Posted from TSR Mobile

Actually I'll do it here if you don't mind.

(1+ax)^n = 1 + 2x + 3/2x^2

Find n and a.

So

2 = na

3 = n(n-1)a^2

This is where I'm at?
Is this right and where next.

Thanks

This is correct now solve as a simultaneous equation. Use the 2=na to express either n or a as the other one and then substitute this value into the 3=n(n-1)a^2 equation

Posted from TSR Mobile

This is correct now solve as a simultaneous equation. Use the 2=na to express either n or a as the other one and then substitute this value into the 3=n(n-1)a^2 equation

Posted from TSR Mobile

Yes got it. Thanks. I did a= 2/n

I have one more. Its multiplication of expansions. They are quite easy but then they have dropped this one on me at the last one. Can you help.

Its 2 parts.

If x- (1/x) = u, find u^3 in terms of x

Hence express x^3 - (1/x^3) in terms of u

I have no clue what this has to do with multiplications that I have just been taught.

Thanks

The first part you just need to do the expansion of (x-1/x)^3 using the n choose r formula.

Second part replace any x with x^3 and compare it to what you is in terms of x

Posted from TSR Mobile

done the first part.

but I used the form (a+b)^n because "a" is not a 1 ?
I got

x^3 - 3x + 3/x - 1/x^3