Binomial Expansion Question?

Then we are told "Given that the third term of this series is 540x²
b) Show that k=6

c) Find the coefficient of x^3"Thing is, I did part a and didn't get 540x²as the third term...

You don't need to give me the answer, if you feel that is me cheating, however I would kindly appreciate somebody pointing me in the right direction! :smile:

Thank you!

Untitled.jpg12.9KB

Scroll to see replies

Reply 1

Chlorophile

Original post by iamabbie97

Thank you!

What's your working?

Reply 2

TeeEm

Original post by iamabbie97

Thank you!

your expansion in part (a) will be in terms of k

then you set that to 540(x²)

Reply 3

iamabbie97

Original post by Chlorophile

What's your working?

Here's a picture, sorry if it isn't very clear...I used the nCr (a)ⁿ(b)0 +nCr (a)^n-1 + (b)¹....

Formula, and then went down and down, I'm not the best with fractions, that might be why

P.S if it looks like an S, it's a 5, if the workings aren't clear to read, let me know and I'll quickly rewrite them :smile:

1975150_1006263669390759_4007535453920729466_n.jpg105.4KB

Reply 4

iamabbie97

Original post by Chlorophile

What's your working?

Here's a far better photo, I'm not even sure what I've done to be honest!

10690203_1006266999390426_4251570750209343634_n.jpg52.5KB

Reply 5

iamabbie97

Original post by TeeEm

your expansion in part (a) will be in terms of k

then you set that to 540(x²)

I've uploaded a picture of my workings, I don't think I've done it right

Reply 6

TeeEm

Original post by iamabbie97

I've uploaded a picture of my workings, I don't think I've done it right

it look correct to me ..

I think you should look at my previous post.

Reply 7

iamabbie97

Original post by TeeEm

it look correct to me ..

I think you should look at my previous post.

So I would put what I've got as my third term equal to 540x²and go from there?

Reply 8

Chlorophile

Original post by iamabbie97

Here's a far better photo, I'm not even sure what I've done to be honest!

That all looks right to me... What did you do next?

Original post by iamabbie97

So I would put what I've got as my third term equal to 540x²and go from there?

Yes, you make (5/2)k^3=540

Reply 9

TeeEm

Original post by iamabbie97

So I would put what I've got as my third term equal to 540x²and go from there?

yes

equate the x² terms

Reply 10

iamabbie97

Original post by Chlorophile

That all looks right to me... What did you do next?

I'm not too sure how to multiple the fractions with the other numbers, for example would the second term be 5xk⁴/2 ?

Reply 11

Chlorophile

Original post by iamabbie97

I'm not too sure how to multiple the fractions with the other numbers, for example would the second term be 5xk⁴/2 ?

Yes, which is the same thing as saying 2.5k^4x. You just multiply.

Reply 12

iamabbie97

Original post by Chlorophile

Yes, which is the same thing as saying 2.5k^4x. You just multiply.

So is this line of workings correct? And would that be the final expansion?

1656006_1006273996056393_8623469508255056577_n.jpg61.8KB

Reply 13

Chlorophile

Original post by iamabbie97

So is this line of workings correct? And would that be the final expansion?

Yes that's right (although obviously there are also more terms and you can simplify the fourth term).

Reply 14

iamabbie97

Original post by Chlorophile

Yes that's right (although obviously there are also more terms and you can simplify the fourth term).

Can I simplify it by dividing the 10 and 8 by 2? And would I be able to do that to the third term as well?

Reply 15

Chlorophile

Original post by iamabbie97

Can I simplify it by dividing the 10 and 8 by 2? And would I be able to do that to the third term as well?

Well 10/4 = 5/2 and 10/8 = 5/4 so yes!

Reply 16

iamabbie97

Original post by Chlorophile

Well 10/4 = 5/2 and 10/8 = 5/4 so yes!

Thank you so much for your help! :smile:

Reply 17

iamabbie97

Original post by Chlorophile

Well 10/4 = 5/2 and 10/8 = 5/4 so yes!

How do I find the coefficient of x³?

Reply 18

Chlorophile

Original post by iamabbie97

How do I find the coefficient of x³?

Well you know what k is so it's just a matter of subbing it in to the expression you've already got. The coefficient is the constant you're multiplying the x^3 by.