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1. Binomial Expansion
Hi,

A few months ago, I begun the AS Maths course so I am quite new to the advanced level of maths, and I am really struggling with understanding the Binomial Expansion :/

Any help at all related to this topic would be much appreciated since I am really clueless! [I've also heard that this is one of the easiest topics which is quite worrying!]

Thank you (:
2. Re: Binomial Expansion
What don't you understand about it?
3. Re: Binomial Expansion
(Original post by cpdavis)
What don't you understand about it?
I don't get what the long equation is for, and how you use it. I know you're not supposed to write out Pascals triangle because it would take too long, but I don't understand how to use the alternative. For example, I can work out (x+1)^10 using Pascal's triangle but not by using the formula.

And I haven't been taught this properly yet since I'm in year 11, but I'm apparently supposed to make sense of it myself which is annoying. And I probably sound really stupid since I don't know what I'm talking about exactly. >.<
4. Re: Binomial Expansion
(Original post by x-Sophie-x)
Hi,

A few months ago, I begun the AS Maths course so I am quite new to the advanced level of maths, and I am really struggling with understanding the Binomial Expansion :/

Any help at all related to this topic would be much appreciated since I am really clueless! [I've also heard that this is one of the easiest topics which is quite worrying!]

Thank you (:
Well, in its simplest form it's all about understanding what the powers of (1 + x) look like, so:

etc

You can generalise this in various ways to look at powers of 1 + ax or integer (whole number) powers of x + y, or even fractional powers of two terms in a bracket, but this leads to infinite series which you might not have come across yet.

What are you having problems with at the moment?
5. Re: Binomial Expansion
(Original post by x-Sophie-x)
I don't get what the long equation is for, and how you use it. I know you're not supposed to write out Pascals triangle because it would take too long, but I don't understand how to use the alternative. For example, I can work out (x+1)^10 using Pascal's triangle but not by using the formula.

And I haven't been taught this properly yet since I'm in year 11, but I'm apparently supposed to make sense of it myself which is annoying. And I probably sound really stupid since I don't know what I'm talking about exactly. >.<
Sorry, just seen your edit after I finished typing my previous answer!

The "long formula" should just give you the same numbers from Pascal's triangle. Do you know how to work out factorials etc so you can calculate the binomial coefficients?
6. Re: Binomial Expansion
(Original post by davros)
Sorry, just seen your edit after I finished typing my previous answer!

The "long formula" should just give you the same numbers from Pascal's triangle. Do you know how to work out factorials etc so you can calculate the binomial coefficients?
Ah okay, thank you. And sorry about that!

Oh it does? -.- Woops, I think I need to look at it again more closely.

Nope, I don't even have a clue about what factorials are!

7. Re: Binomial Expansion
(Original post by davros)
Well, in its simplest form it's all about understanding what the powers of (1 + x) look like, so:

etc

You can generalise this in various ways to look at powers of 1 + ax or integer (whole number) powers of x + y, or even fractional powers of two terms in a bracket, but this leads to infinite series which you might not have come across yet.

What are you having problems with at the moment?
I do understand this, and I get how it's done with powers of x and y.

But how does the formula help with solving say, (x+1)^10 ?
I know how to solve it using Pascal's triangle.
8. Re: Binomial Expansion
(Original post by x-Sophie-x)
I do understand this, and I get how it's done with powers of x and y.

But how does the formula help with solving say, (x+1)^10 ?
I know how to solve it using Pascal's triangle.
Are you aware of this formula?

In this case, with your expansion of x and y, replace your y with 1
9. Re: Binomial Expansion
(Original post by cpdavis)
Are you aware of this formula?

In this case, with your expansion of x and y, replace your y with 1
Indeed.

Ah that makes a little more sense now, thank you.
10. Re: Binomial Expansion
(Original post by x-Sophie-x)
Ah okay, thank you. And sorry about that!

Oh it does? -.- Woops, I think I need to look at it again more closely.

Nope, I don't even have a clue about what factorials are!

n factorial is written as n! and basically all it means is

n! = n x (n-1) x (n-2) x ... x 2 x 1

So start with n then multiply by the next number below..then the next...and so on til you get to 1.

You need them to calculate the binomial coefficients (unless you use the nCr button on your calculator )
11. Re: Binomial Expansion
(Original post by -G-a-v-)
n factorial is written as n! and basically all it means is

n! = n x (n-1) x (n-2) x ... x 2 x 1

So start with n then multiply by the next number below..then the next...and so on til you get to 1.

You need them to calculate the binomial coefficients (unless you use the nCr button on your calculator )
Oh right! Thanks, I get it now!