How do I prove orthogonality if the lengths of two vectors are equal?

Question

If $||v|| = ||w||$, how can we show $(v + w)$ and $(v - w)$ are orthogonal?

I can't find a way to show $(v + w) * (v + (- w)) = 0$

Answer 1

$$(v+w)\cdot (v-w)= v\cdot v - v\cdot w + w\cdot v - w\cdot w = \Vert v \Vert^2 - v\cdot w + w\cdot v - \Vert w \Vert ^2 $$ But $ \Vert v \Vert^2 = \Vert w \Vert^2$ and $w\cdot v = v\cdot w$ so $$(v+w)\cdot (v-w) = 0$$