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Componendo and Dividendo

Prove that ...

Question

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

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Solution

$(\to a - \to b) \times (\to a + \to b) = \to a \times \to b + \to a \times \to b - \to b \times \to a - \to b \times \to b$
$= \to a \times \to b + \to a \times \to b$
$= 2 (\to a \times \to b)$
$(\to a - \to b) \times (\to a + \to b) = 2 (\to a \times \to b)$

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