I know how to compute scalar and cross products but I'm not very familiar with what other rules applies to vectors.

For example If I have the vectors u and v and the following equation $\displaystyle u x (u+v) - v x (3u+v) $ and I know that u x v = {3,1,-1}

how do they arrive at 4uxv when simplifying the equation? Also in what order should you do the calculations, does cross product come before dot and addition/subtraction?