# problem understanding $a\times((b\cdot b)a-(b\cdot a)b)=-a\cdot ba\times b$

$a\times(b\times(a\times b))=a\times((b\cdot b)a-(b\cdot a)b)=-a\cdot ba\times b$
can anyone expand on how the final answer is derived?
I try to expand but ended up scratching my head.
the best I can do is this
$a\times(ab\cdot b - ab\cdot b)$

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In $a\times((b\cdot b)a-(b\cdot a)b)$, the first term is zero because $a \times a = 0$. This leaves the second term. Note that $a\cdot b = b\cdot a$.
$a\times-(a\cdot b)b$ but how did it end up $-a\cdot ba \times b$?we could just exchange cross and dot operator, right? – kypronite Oct 21 '12 at 14:14
sorry,forget what I said.Just found out about the cross product $(cu)\times v=u\times (cv)$ – kypronite Oct 21 '12 at 14:25