For example, in
In the left-hand side of the first equation, the 2 multiplies the sum of 1 and 3; on the right-hand side, it multiplies the 1 and the 3 individually, with the products added afterwards.Because these give the same final answer (8), multiplication by 2 is said to distribute over addition of 1 and 3.Since one could have put any
∗ is left-distributive over + if,
∗ is right-distributive over + if, given any elements x, y, and z of S,
∗ is distributive over + if it is left- and right-distributive.