How ca I prove that in a real/complex vector space V

$\displaystyle ||x + y||^{2}+ ||x - y||^{2} = 2(||x||^{2} + ||y||^2)$

Also If I consider the parallelogram

with adjacent sides OP; OQ where P is the point (x1; x2); Q is the point (y1; y2) and O is

the origin.What does this say about a parallelogram in the plane?

This is an exercisse from LINEAR ALGEBRA AND ITS APPLICATIONS David C. Lay.