Brownian motion square

Question

I need to calculate for Brownian motion $dBt^2$ and $dBt^4$. For $dBt^2$, I think that it is correct to use Ito's lemma.

So we get: $$ dBt^2=(1/2)\cdot 2 \cdot dt +2\cdot Bt\cdot dBt$$

Is this correct?

What about $dBt^4$?