Binomial expansion with negative power

Hi I'm losing it aren't I. Yes, I've sent the photo of one question and the answer to a different one. And now, although the % error was not required in the actual question, I've tried it and it's much nearer. Thank you so much and very well spotted.

Just post your new working if youre still unsure.

Thanks, but I'm fully with it now. I was comparing my answer to question 15 in Mixed Exercises C whilst actually attempting the Paper 2 question 9. No wonder they didn't match. All is sorted now. Silly me.

Good. Im not too sure of how youre taught it, but another way (for the wrong question) is
1/2 * (9x^2+26x+20) * (1 + (3x+x^2)/2)^(-1)
and you can do the binomial series for (1 + (3x+x^2)/2)^(-1) where the usual x is replaced by (3x+x^2)/2 and then multiply that by (9x^2+26x+20) (and 1/2) to get the result
Id guess they want you to do it your way as theyve given you the denominator factorised. Its a bit of an algebra slog whichever way you do it.

There is a slight danger to expand that way, because of radius of convergence issues.
But all is good here - we just need to justify that |(3x+x^2)/2| < 1 indeed implies |x|<1, which is probably not required in A-Levels anyway.