# Thread: More help with Binomials

1. ## More help with Binomials

Well after isomorphism helped get me sorted out the other day I thought I had these Binomials licked BUT!!!!

When I tried this one I couldn't seem to get the right answer

Find the term x^44 in the following

(x^2 - 1/sq root x)^27

So thought I was doing well getting

this as the general term

(27 over r) ( x^2n-2r ) . (-x^-1/2r)

and the solving for r ie 5/2r = 27 but then of course r works out really ugly.

If someone prepared to have a go at helping I would be grateful

2. $\displaystyle T_{k+1}=(-1)^kC_{27}^k(x^2)^{27-k}\left(x^{-\frac{1}{2}}\right)^k=(-1)^kC_{27}^kx^{\frac{108-5k}{2}}$
Then $\displaystyle \frac{108-5k}{2}=44\Rightarrow 5k=20\Rightarrow k=4$

3. Thanks

If the two components are different which one does one use when solving for r. Do you have nay general tips since I think that's the part I am struggling with?