Proving a given vector equation

Homework Statement

Prove ||u+v||^2 + ||u-v||^2=2||u||^2+2||v||^2

Homework Equations

* This is the part I can't figure out*

The Attempt at a Solution

anybody got an idea where I can start? I can't seem to remember the property I can use to simplify ||u+v||^2

P.S sorry for the vague title, i really didn't know what to put in there.

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jedishrfu
Mentor
Are u and v vectors?

Yes! sorry I should have italized them , copy pasted it, Ill edit it right now

jedishrfu
Mentor
What can you say about u+v and u-v?

Hmmmm, Not too sure what I can say, but geometrically they are two sides of a parallelogram, and u+v / u-v is the line across it

jedishrfu
Mentor
Have you tried using the vector dot product for u+v and for u-v?

Hint replace the (u+v)^2 with its dot product

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Ahhh I see so I do u+v dot u+v ? then just distribute and use the idea that u dot u = ||u||?

jedishrfu
jedishrfu
Mentor
I think you have it now. I hope my hint wasn't too obvious.

MarcL
nope lead me in the right direction. Thank you so much!