Integer Multiplication Distributes over Addition/Corollary

Corollary to Integer Multiplication Distributes over Addition
The operation of multiplication on the set of integers $\Z$ is distributive over subtraction:


 * $\forall x, y, z \in \Z: x \times \paren {y - z} = \paren {x \times y} - \paren {x \times z}$
 * $\forall x, y, z \in \Z: \paren {y - z} \times x = \paren {y \times x} - \paren {z \times x}$