 ##  [Distributive Law](/distributive-law) 

  ##  [Distributive Law](https://mathlogic.quantumdictionary.io/distributive-law-0) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

The equivalences that relate two binary operators by distributing one over the other; in Boolean logic the two forms are A ∧ (B ∨ C) ↔ (A ∧ B) ∨ (A ∧ C) and A ∨ (B ∧ C) ↔ (A ∨ B) ∧ (A ∨ C).

 
 ##  [Distributive Law](https://puremath.quantumdictionary.io/distributive-law-1) 

  
 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

A compatibility law between two binary operations · and + on a set stating that a·(b + c) = a·b + a·c and (b + c)·a = b·a + c·a for all elements, so one operation distributes over the other.

 
 ##  [Distributive Law](https://algebra.quantumdictionary.io/distributive-law-2) 

  
 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 
Definition

A relation between two binary operations showing that one operation distributes over the other, typically written as a·(b + c) = a·b + a·c (left distributivity) and (b + c)·a = b·a + c·a (right distributivity) when both hold.