ImBadAt
Badges: 3
Rep:
?
#1
Report Thread starter 4 weeks ago
#1
I know that the genral formular for binomial expansion with rational powers is: (1+x)^n= 1+nx+n(n-1)/2! and so on.
However I dont under stand how the first and second terms of the expansion are 2 and 5/4x. Surely they should be 4 and 5/2x as n in this case is 1/2 and x is 5x. What am i doing wrong here?
0
reply
Maths Fan
Badges: 9
Rep:
?
#2
Report 4 weeks ago
#2
Can you show the working and I can highlight the error ? I’m assuming you may have taken the 4 out of the brackets but not taken the power with it….?
0
reply
RogerOxon
Badges: 21
Rep:
?
#3
Report 4 weeks ago
#3
(Original post by ImBadAt)
I know that the genral formular for binomial expansion with rational powers is: (1+x)^n= 1+nx+n(n-1)/2! and so on.
However I dont under stand how the first and second terms of the expansion are 2 and 5/4x. Surely they should be 4 and 5/2x as n in this case is 1/2 and x is 5x. What am i doing wrong here?
You want to expand (4-5x)^{\frac{1}{2}}, but your formula is to expand (1+x)^n. It's fairly obvious that you can replace x with something else, but not the 1. You need to manipulate your initial equation, to get it into the form of your second one. To do this, you need to make that 4 a 1 - how are you going to do that?
Last edited by RogerOxon; 4 weeks ago
0
reply
ImBadAt
Badges: 3
Rep:
?
#4
Report Thread starter 4 weeks ago
#4
(Original post by Maths Fan)
Can you show the working and I can highlight the error ? I’m assuming you may have taken the 4 out of the brackets but not taken the power with it….?
4+(1/2)(5x)+1/2(-1/2)*x^2/2! for the first 3 terms

so should it be 4^1/2 as the first term giving 2. But then how is 5/4x made?
Last edited by ImBadAt; 4 weeks ago
0
reply
Maths Fan
Badges: 9
Rep:
?
#5
Report 4 weeks ago
#5
So from your working I can see you’ve not manipulated the bracket correctly at the start.
(4-5x)^1/2 , needs to be changed so it’s in the required form to continue if that makes sense?
0
reply
ImBadAt
Badges: 3
Rep:
?
#6
Report Thread starter 4 weeks ago
#6
(Original post by Maths Fan)
So from your working I can see you’ve not manipulated the bracket correctly at the start.
(4-5x)^1/2 , needs to be changed so it’s in the required form to continue if that makes sey
Yes that makes sence, Thankyou. I needed to factor out ther 4 right?
Last edited by ImBadAt; 4 weeks ago
0
reply
Maths Fan
Badges: 9
Rep:
?
#7
Report 4 weeks ago
#7
Yes correct and don’t forget the power should go with it.
0
reply
Muttley79
Badges: 20
Rep:
?
#8
Report 4 weeks ago
#8
(Original post by ImBadAt)
Yes that makes sence, Thankyou. I needed to factor out ther 4 right?
Don't forget the power too ...
0
reply
ImBadAt
Badges: 3
Rep:
?
#9
Report Thread starter 4 weeks ago
#9
(Original post by Muttley79)
Don't forget the power too ...
ok so i factor out 4^1/2 which is 2. I then do the expansion of (1+5/2x)^1/2. And im assuming that at the end i would multiply all the terms by 4^1/2?
0
reply
Muttley79
Badges: 20
Rep:
?
#10
Report 4 weeks ago
#10
(Original post by ImBadAt)
ok so i factor out 4^1/2 which is 2. I then do the expansion of (1+5/2x)^1/2. And im assuming that at the end i would multiply all the terms by 4^1/2?
Inside the bracket it will be 5x/4 but otherwise correct.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

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

Personalise

Have you made your mind up on your five uni choices?

Yes, and I've sent off my application! (233)
57.25%
I've made my choices but havent sent my application yet (52)
12.78%
I've got a good idea about the choices I want to make (45)
11.06%
I'm researching but still not sure which universities I want to apply to (36)
8.85%
I haven't started researching yet (23)
5.65%
Something else (let us know in the thread!) (18)
4.42%

Watched Threads

View All