# Product

A mathematical product is a term that describes the result of multiplication. This is true of both numbers as well as expressions. In the expressions below,

(1) | 4 × 3 | = | 12 |

(2) | (x + 1)x^{2} |
= | (x^{2} + x^{3}) |

12 is the product in (1), and in (2), the product is (x^{2} + x^{3}).

The term product is widely used throughout many different mathematical contexts. Some are closely related to arithmetic multiplication while others, like the product of two matrices, tensor products, cross products in 3D space, etc, can be far more complex.

### Product of natural numbers

The first example, (1), above is an example of a product of natural numbers, one of the simplest types of product. Natural numbers cannot be negative (some definitions include 0 but others may only use the counting numbers). The product of natural numbers is just the result of a multiplication problem.

### Product of integers

The product of integers is mostly the same as the product of natural numbers, except that negative values can be included. Below are the rules for multiplying positive and negative integers.

- Positive * Positive = Positive
- Negative * Negative = Positive
- Positive * Negative = Negative
- Negative * Positive = Negative

Essentially, if there are an odd number of negative signs in the multiplication problem, the resulting value will be negative; if there are a positive number of negative signs, the number will be positive. The number of positive signs does not matter.