Expectations of Brownian motion (simple, I hope)

[AxiomOfChoice]

Let B_t be Brownian motion in \mathbb R beginning at zero. I am trying to find expressions for things like E[(B^n_s - B^n_t)^m] for m,n\in \mathbb N. So, for example, I'd like to know E[(B^2_s - B^2_t)^2] and E[(B_s - B_t)^4]. Here are the only things I know:

1. E[B_t^{2k}] = \frac{(2k)!}{2^k \cdot k!}
2. E[B_s B_t] = \min(s,t)
3. E[(B_s - B_t)^2] = |s-t|
4. Brownian motion has independent increments.

But I'm having a hard time getting expressions for the expectations I listed in the start of the question using these facts. Can someone help?

 

[AxiomOfChoice]

For example, in trying to compute E[(B_s - B_t)^4], one comes up against things like 4E[B_s^3B_t]. How in the world am I supposed to deal with that?