Example

Let (R,+,*,0,1) be a ring. The laws lead to rules for calculations which are known from the usual examples.

For instance, if, in a product, one factor is 0, then the whole product is 0.

Another example:

(-a₁) (-a₂) · · · (-a_n) = (-1)ⁿ (a₁a₂ · · · a_n).