x Turn on thread page Beta
 You are Here: Home >< Maths

# Binomial expansion watch

1. How would you expand (1-x^2)^1/2 ?
It doesn't seem to fit into either of the forms as n isn't a positive integer and the x is squared
2. (Original post by G.Y)
How would you expand (1-x^2)^1/2 ?
It doesn't seem to fit into either of the forms as n isn't a positive integer and the x is squared
When n is negative or a fraction, you do it differently:

E.g. (1 + bx)^n

1 + (bx)(n) + ((n)(n-1)(bx)^2)/2! + ((n)(n-1)(n-2)(bx)^3)/3! ...

Tip: If the number inside the bracket is not 1 ( e.g. (2 + bx)^n), then take the number out to make the number inside one.

E.g. (2 + bx)^n = 2^n (1 + bx/2)^n

I did this about a month ago so not exactly experienced lol. But hope I helped!

And btw, the x^2 in the question doesn't make a difference to the method I shown above.
3. (Original post by G.Y)
How would you expand (1-x^2)^1/2 ?
It doesn't seem to fit into either of the forms as n isn't a positive integer and the x is squared
Either,

in your expansion where you'd normally have x, you want to put x^2, or,

Let y=x^2

Then expand (1+y)^1/2

And when you have your series, substitute x^2 for the y.
4. (Original post by ghostwalker)
Either,

in your expansion where you'd normally have x, you want to put x^2, or,

Let y=x^2

Then expand (1+y)^1/2

And when you have your series, substitute x^2 for the y.
(Original post by C_Yap)
When n is negative or a fraction, you do it differently:

E.g. (1 + bx)^n

1 + (bx)(n) + ((n)(n-1)(bx)^2)/2! + ((n)(n-1)(n-2)(bx)^3)/3! ...

Tip: If the number inside the bracket is not 1 ( e.g. (2 + bx)^n), then take the number out to make the number inside one.

E.g. (2 + bx)^n = 2^n (1 + bx/2)^n

I did this about a month ago so not exactly experienced lol. But hope I helped!

And btw, the x^2 in the question doesn't make a difference to the method I shown above.
So the x^2 changes nothing? Thanksssss

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 6, 2018
Today on TSR

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams