Where $A$ and $B$ are vectors, and $\times$ is the cross product operator. I was able to get $A(A \cdot B) - B$ using the vector triple product, but it doesn't look like a simplified version to me.
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Firstly note that, the vector triple product you want to evaluate is actually: $$A \times (A \times B)=(A\cdot B)A-(|A|^2)B$$
And this is, in fact, the most simplified expression that we can arrive at with what little you have given us!