distributive

If + and \(\cdot \) are binary operations on a given set, then we say that \(\cdot \) is left-distributive over + if for any elements \(a\), \(b\), and \(c\) in the set we have \(a\cdot (b+c)=a\cdot b+a\cdot c\). Similarly we say that \(\cdot \) is right-distributive over + if for any elements \(a\), \(b\), and \(c\) in the set we have \((b+c)\cdot a=b\cdot a+c\cdot a\). If \(\cdot \) is both left and right distributive over + then we say simply that it is distributive over +.

The fact that in arithmetic multiplication is distributive over addition is referred to as the distributive property of arithmetic.