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# Prove that $(a - b) \times (a + b) = 2 (a \times b)$.

## $=2(\mathbf{a} \times \mathbf{b})$

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Welcome back to another cross product problem where we're trying to prove an identity involving A minus B. Cross A plus B. We'll break this down into a couple steps. We know that first we can distribute using the cross product and so that this is equivalent to a minus B. Cross A plus A minus B. Cross B. Once again, we can distribute across cross products, meaning this is the same as a cross A minus B. Cross A plus a cross B minus B craft, and we could have done that all in one step, if we wanted to, will notice that any vector across itself is equal to zero and negative be cross A is the same thing as a Crosby. So we have another A Crosby. Any vector cross itself is zero. We're left with a cross B plus a Crosby, which is to a cross B, which is the identity that we wanted to show. Thanks for what.

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