distributivity

Distributivity is the mathematical property of interaction between operations.

Formally,
for a set $S$ and two binary operations $+$ and $\times$ on $S$ ,
the operation $\times$ is left-distributive over $+$ if

x \times (y + z) = (x \times y) + (x \times z) \forall x, y, z \in S

the operation $\times$ is right-distributive over $+$ if

(y + z) \times x = (y \times x) + (z \times x) \forall x, y, z \in S

the operation $\times$ is distributive over $+$ if it is both left- and right-distributive.

The two equations above constitute the distributive property.
When $\times$ is commutative, they are logically equivalent.