For arbitrary natural numbers \(n,m,p\in\mathbb N\) with the binary operations addition "\( + \)" and multiplication "\(\cdot\)", the following distributivity laws hold:
\[\begin{array}{ccl} (n+m)\cdot p&=&(n\cdot p)+(m\cdot p)\quad\quad\text{"right-distributivity property"},\\ p\cdot(n+m)&=&(p\cdot n)+(p\cdot m).\quad\quad\text{"left-distributivity property"}\\ \end{array}\]
Proofs: 1
