For arbitrary integers \(x,y,z\in\mathbb Z\) with the binary operations addition "\( + \)" and multiplication "\(\cdot\)", the following distributivity laws hold:
\[\begin{array}{ccl} x\cdot(y+z)&=&(x\cdot y)+(x\cdot z).\quad\quad\text{"left-distributivity property"}\\ (y+z)\cdot x&=&(y\cdot x)+(z\cdot x)\quad\quad\text{"right-distributivity property"},\\ \end{array}\]
Proofs: 1
