This is a strange request, but still.
I encountered this kind of expression: $$ v_1+v_2+v_1\times v_2 $$ If these were numbers, I would profitably rewrite this as $$ (1+v_1)\times(1+v_2)-1 $$ but of course this is impossible: there is no nonzero vector $1$ with $1\times1=1$, let alone $1\times v=v\times1=v$ for all $v$.
Do you know of any kind of substitute for that? To be more specific, can one rewrite $v_1+v_2+v_1\times v_2$ as $x+y_1\times y_2$ where $y_i$ only depend on $v_i$ while $x$ does not depend on anything?