C2 vs C4 binomial expansion

What is new in C4's binomial expansion compared to C2? I thought the actual expansion was only in C4, but I see that the formula is under C2 in the formula booklet and is also in the C2 textbook?

Or is it just the small point about when n is less than 1?

Reply 1

TenOfThem

18

Original post by jon889

What is new in C4's binomial expansion compared to C2? I thought the actual expansion was only in C4, but I see that the formula is under C2 in the formula booklet and is also in the C2 textbook?

Or is it just the small point about when n is less than 1?

Fractional and negative n is the only new element

Reply 2

gdunne42

21

and although it's not new, many C4 questions will require you to factorise before you start so you can use the (1+x)^n expansion. This factorisation usually isn't needed in C2 where you can generally use the (a + b)^n expansion.

e.g. (4+x)^0.5 = [4(1 + x/4)]^0.5 = 2[(1 + x/4)^0.5]

Reply 3

alzy1

How does the the binomial formula differ in C4, and can you use the nCr method on C4 questions??

Reply 4

TenOfThem

18

Original post by alzy1

How does the the binomial formula differ in C4, and can you use the nCr method on C4 questions??

If you understand nCr then yes

If it is just a button on you calculator then no

Reply 5

alzy1

Its because, it does not mention the nCr method within the C4 textbooks what so ever. So the only thing extra to learn for C4 is expanding using negative and fractional powers??

Reply 6

XxKingSniprxX

21

Original post by alzy1

Its because, it does not mention the nCr method within the C4 textbooks what so ever. So the only thing extra to learn for C4 is expanding using negative and fractional powers??

Yes that's true, but there is also the C4 bit on Binomial expansion - validity.

If the power 'n' is not a positive integer then the series is infinite and only valid for -1<a<1.

Reply 7

john122334455

In the C4 content. They teach us to factorise expressions in order to achieve the form: (1+x)^n

For example if we had: (2+6x)^5, factorise to 2[(1+3x)]^5

Why do we have to factorise, we learnt in C2 to expand any expression in the form (a+b)^n.

Reply 8

gdunne42

21

Original post by john122334455

In the C4 content. They teach us to factorise expressions in order to achieve the form: (1+x)^n

For example if we had: (2+6x)^5, factorise to 2[(1+3x)]^5

Why do we have to factorise, we learnt in C2 to expand any expression in the form (a+b)^n.

First, you have an error in your factorisation
It should be

[2(1+3x)]^5
That is
2^5(1+3x)^5

You usually have to factorise in C4 because the (a+b)^n expansion only works for positive integer values of n and in C4 you are generally working with negative, fractional or unknown powers.

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(edited 9 years ago)

C2 vs C4 binomial expansion

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