Universal enveloping algebra of sl(2)

Question

This exercise is regarding universal enveloping algebra of $sl(2,F)$. Let $L=sl(2,F)$ with standard basis $\{x,y,h\}$. First to show that $1-x$ is not invertible in $U(L)$. That I proved. Let $I$ br a maximal left ideal in $U(L)$ which contains $1-x$. Let $V=U(L)/I$ and it is an $L$ module. To prove that the images of $1,h,h^2, \ldots$ are linearly independent in $V$ using the identity $(x-1)^rh^s \equiv 0(mod ~~I) ~~ if~~ r>s$ or $\equiv (-2)^r r!.1$ if $r=s$. I am not able to proceed please help me. I am stuck in some part of the identity when $r=s$. I am not getting the term $r!$. Please help me.. $((x-1)h)^r=(xh-h)^r=(hx-h-2x)^r=(h(x-1)-2x)^r \equiv (-2x)^r mod ~~I~~$. How to proceed further?