Prove that `( vec(A) + vec(B)) xx ( vec(A) - vec(B)) = 2 (vec(B) xx vec(A))`

Explanation

To prove that \(( \vec{A} + \vec{B}) \times ( \vec{A} - \vec{B}) = 2 ( \vec{B} \times \vec{A})\), we can follow these steps:

### Step 1: Expand the Left-Hand Side (LHS)
We start with the expression on the left-hand side:
\[ (\vec{A} + \vec{B}) \times (\vec{A} - \vec{B}) \]
Using the distributive property of the cross product, we can expand this:
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