The process of factorization of algebraic polynomials is fundamentally a process called distributive groups factorization. The following example serves to illustrate this methodology.

In the study of algebra, it is well known that the factor of x-y is (x-y)(x+y). Since multiplication is commutative, the factors can also be written as (x+y)(x-y), showing that the orders of the factors do not affect the outcome of the binary operation. However, by distributive grouping, first it is necessary to provide two addends –xy and +xy whose sum is zero such that x-y= x-y-xy+xy. Then one possible grouping is given as (x-xy)+(xy-y). The common factor of the first term is x and the common factor of the second term is y. By factoring these two common factors gives x(x-y)+y(x-y). This last algebraic expression has the common factor (x-y). Again, by factoring this common factor gives (x-y)(x+y). If both x and y represent the different squares of energy E such that x is not always equal to y then the totality of the quantized space-time continuum as squares of zero-point energies of the quantum vacuum fluctuations can be analyzed by using distributive groups factorization. Odd groupings give mass and even groupings give first power of energy.