Assuming that the average value m of two numbers is fixed and d is the difference between the two numbers and the average value, then a = m+d and b = m-d.

ab = (m + d)(m - d) = m^2 - d^2

It can be seen that the smaller d (that is, the closer two numbers are to the average, that is, the smaller the difference between two numbers), the greater the product.

The concept of product depends on the definition of "multiplication". When people upgrade the set of multiplication objects to more general sets, such as groups, rings, fields, etc. The concept of the product will also change.

Let A be a set, we define the multiplication F:A ×A→A, that is, the mapping of A and its own cartesian product to A, and let (x, y)∈A×A, then we call the pixel F(x, y) the product of x and y, abbreviated as xy.

The concept of product of algebraic structure is often used when studying algebraic structure in abstract algebra. The product of two algebraic structures is generally defined as a new algebraic structure in which the elements in the two algebraic structures correspond to a new element through a binary mapping, and then the new element is formed through appropriate rules.

If the number of elements of two algebraic structures is limited, then the number of elements of their product will be the product of their respective elements. This is one of the reasons why this new algebraic structure is called product.