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Prove that ( vec(A) + vec(B)) xx ( vec(A...

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

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`(vec(A) + vec(B)) xx (vec(A) - vec(B)) = vec(A) xx vec(A) - vec(A) xx vec(A) -vec(A) xx vec(B) + vec(B) xx vec(A) - vec(B) xx vec(B)`
`vec(A) xx vec(A) = vec(B) xx vec(B) = 0 and vec(A) xx vec(B) = - (vec(B) xx vec(A))`
`(vec(A) + vec(B)) xx (vec(A) - vec(B)) = 0 - [-(vec(B)xx vec(A))] + vec(B) xx vec(A) - 0 `
` = 2(vec(B) cxx vec(A))`
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