Hi.

So, here's the set up. I have 3 equations:

And my task is to show that:

I can give the same equations using alternative variables if it makes it easier on the eyes for you:

Show that:

My Question

Is there a way to do this that doesn't involve actually having to square B, and muliply A and C, leading to a disturbingly large number of terms in the equation?

I feel like there should be a way to exploit the symmetry of the equations to create factors which allow me to deduce the final result in a vastly reduced number steps with an appropriate number of terms in my derivation.

I should stress that this is not a homework piece, but a small part of a much larger derivation that I am doing for practice, and wonder if it can be economised.