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> Given a beta distribution $f (y)=2 (1-y)$ and $C=10+20Y+4Y^2$, find $\mbox{Var} [C]$. 
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I already know $\alpha=1$ and $\beta=2$, so $\mu =\frac13$ and $\sigma^2=\frac{1}{18}$.

I also found that $\mathbb{E} (C)=\frac{52}{3}$ using the fact that $\mathbb{E} (aY+b)=a\mathbb{E} (Y)+b$. I tried calculating $\mathbb{E} (C^2)-[\mathbb{E} (C)]^2$ but got stuck because didn't know how to do $E [aY^3]$ or $E [aY^4]$. 

Can anyone help? This is problem 4.97 in Wackerly 6th ed, btw.