---
tags:
  - Mathematics
  - Prealgebra
  - theorems-axioms-laws
---

# The Distributive Property of Multiplication

**Let $a$, $b$ represent members of $\mathbb{W}$ or $\mathbb{Z}$ then:**

$$ a \cdot (b + c) = a \cdot b + a \cdot c $$

### Demonstration

When faced with $4(2\cdot3)$ we may proceed with the official order of operations in algebra, namely:

````
4 x (2 + 3) = 4 x (5)
= 20
````

In other words we find the sum of the values in parentheses and then multiply this by the value outside of the brackets.

When we use distributive property we *distribute* each value in the parentheses against the value outside of the parentheses:

````
4 x (2 + 3) = (4 x 2) + (4 x 3)
8 + 12 = 20
````
