C4 binomial expansion

You have to use the second part to do the third. What happens if you let x=1/3 in the 2nd expansion you got?

As said above. If x=1/3 then you have (from the second part of the question) (8+3(1/3))^{1/3} =

okay i see. thanks

could someone explain why the 'second part' of the question can be used? i.e. the 8+3x inside brackets

what is not valid about (1+8)^1/3 = 9^1/3 ?

I'm sure you've learnt that the binomial expansion of $(1+x)^n$ for non-integer $n$ is only valid for $|x| \leq 1$. It should be written in your formula booklet as well, next to the expansion.

Sooo, can't really plug in $x=8$.

On the other hand $(8 + 3x)^{1/3}$ is valid for $|3x| \leq 1$ so $x=1/3$ is perfectly valid here.

Ahh I see thanks; have learnt that but it was a bit abstract and didn't care aha