In my recent study, I encounter the following problem:

```
{A,B,C,D}::NonCommuting.
ex:=A B (a-b)+B A (b-a)+A C (a-c)+C A (c-a)+B C (b-c)+C B (c-b);
```

How to simplify the expression above? i.e. get the result $$ (AB-BA)(a-b)+(AC-CA)(a-c)+(BC-CB)(b-c) $$