DSP interview question: use of the identity in development of a significant transform

I'm preparing interview and found this question. But I don't really understand what is the question. Does it ask about Fourier transform or Z transform?

How the simple identity

$$xy=\frac{1}{2}x^2 + \frac{1}{2}y^2 - \frac{1}{2}(x - y)^2$$

was used in developing a significant transform in digital signal processing?

• "How? With a great deal of ingenuity, of course!" :-) – Dilip Sarwate Oct 29 '14 at 13:11
• Hi did you find the answers? – gmotree Jun 8 '15 at 15:22