A first observation is that all the extant laws of physics are of product forms. This phenomenon is somewhat intriguing. The question is: why do law of physics always take, instead of a sum of two terms, sum-of-multiple-term (i.e., product) forms?
Counterexample exists in other disciplines of natural sciences. For example, biology has the White's formula (http://www.maths.ed.ac.uk/~aar/papers/eggar.pdf). Since mathematics investigates every possibility, certainly it has results involving sum of exactly two terms.
I am seeking after a reason other than technical reasons. For example, the importance of Lorentz transformation in physics does not lie in its mathematical necessity but in its physical implications, as revealed by A. Einstein. H. Poincare, E. Mach, and several others had realized the concept of relativity before Einstein, but, as the paper ``The structure of thoughts'' (For now I cannot recall the exact title) published in Nature points out, discerning a concept is not equivalent to discerning its meaning. It is Einstein that discerns the meaning of relativity.