Proof of Lagrange's Identity

[cordyceps]

1. The problem statement, all variables and given/known data
Prove Lagrange's identity for real numbers

http://mathworld.wolfram.com/LagrangesIdentity.html

3. The attempt at a solution

I tried one of the methods used in proving the Cauchy-Schwarz inequality (Ax^2 + Bx + C is greater than or equal to zero, where a = the sum from k=1 to n of (ak)^2, b = the sum from k=1 to n of (ak*bk), and c = the sum from k=1 to n of (bk)^2), but I couldn't get very far because I don't understand the last term of the equation's right side. Anyone have any ideas on how to start the problem? Thanks.

[cordyceps]

All that was given in the textbook was a proof of the cauchy-schwarz inequality. The binet-cauchy identity, which was used in some of the proofs I glanced at, was never mentioned.