# Binomial ExpansionWatch

Announcements
#1
Hi there. Stuck on this last question and finding it tricky

Find the term indepenedant of y in each of the following expansions
a)

a)

All helps and hints appreciated
0
11 years ago
#2
When you have a term independent of y, the powers of y will cancel out.
Personally, I'd rewrite it as (y - y-1)^8, so for which term will these cancel out? Then find out what this value is, ie it would've been the coefficient of x for this term.

The second one is a little more tricky, but shouldn't be too difficult.
0
11 years ago
#3
a) A term independent of y will need the y^a and the (-1/y)^b to cancel.
a+b=8
0
#4
I still cant' solve a =(
0
11 years ago
#5

You know that the binomial expansion follows:

So for part a) You will have:

Now, from that, can you get a general expression for what each term in the binomial expansion will be?

If you do, can you think of what you would need to equate it to in order to find out the r-value for the term which is independant of y?
0
#6
(Original post by Square)

You know that the binomial expansion follows:

So for part a) You will have:

Now, from that, can you get a general expression for what each term in the binomial expansion will be?

If you do, can you think of what you would need to equate it to in order to find out the r-value for the term which is independant of y?
Oh lawd, I'm stuck.

Heres was my thought process
(8C0) (y)^8 (y^-1)=8
(8C1) (y)^7 (y^-1)^1
...etc until (8C8)
What am I doing wrong?
0
11 years ago
#7
(Original post by MilesB)
Oh lawd, I'm stuck.

Heres was my thought process
(8C0) (y)^8 (y^-1)=8
(8C1) (y)^7 (y^-1)^1
...etc until (8C8)
What am I doing wrong?
Write out the 8C4 term and see what happens.
0
11 years ago
#8
(Original post by notnek_01)
Write out the 8C4 term and see what happens.
That kind of ruins it
0
11 years ago
#9
(Original post by Square)
That kind of ruins it
Couldn't think of any other hints to give.
0
#10
(Original post by notnek_01)
Write out the 8C4 term and see what happens.
Thank you, was getting hints.
0
#11
I know this is silly but in a Calculator I type for example (8C1) (y)^7 (y^-1)^1
(8C1) x (y)^7 (y^-1)^1
Is the bolded bit typed literally?
0
11 years ago
#12
could you solve the second part? it's not that different really.
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• University of Surrey
Wed, 23 Oct '19
• University of Bristol
Wed, 23 Oct '19
• University of Exeter
Wed, 23 Oct '19

### Poll

Join the discussion

Yes (57)
24.26%
No (178)
75.74%