Integer_Multiplication_Distributes_over_Addition

The operation of multiplication on the set of integers $\Z$ is distributive over addition $\forall x, y, z \in \Z: x \times \paren {y + z} = \paren {x \times y} + \paren {x \times z}$ $\forall x, y, z \in \Z: \paren {y + z} \times x = \paren {y \times x} + \paren {z \times x}$