# Distributive Multiply

The `Distributive Property` can be used for distributing a multiplication across a set of grouped terms. This has the effect of removing a grouping and can expose the terms that were inside for further simplification depending on the problem type.

This rule is expressed by the equation `a(b + c) = ab + ac`

### Transformations¶

Given a multiplication of `a` and `(b + c)` this rule distributes `a` across `b` and `c` leaving only the simpler form of `ab` and `ac`.

`a(b + c) = ab + ac`

``````                             +
*                  / \
/ \                /   \
/   \              /     \
a     +     ->     *       *
/ \          / \     / \
/   \        /   \   /   \
b     c      a     b a     c
``````

### Examples¶

Info

All the examples shown below are drawn from the mathy test suite that verifies the expected input/output combinations for rule transformations.

Input Output Valid
(2 + k^2) * w^4 2w^4 + w^4 * k^2
(1 + k^2) * w^4 1w^4 + w^4 * k^2
(4 + v) * (12 + r) (12 + r) * 4 + (12 + r) * v
(12 + r) * v 12v + v * r
7 * (1 + 1) 7 * 1 + 7 * 1
7x * (2 + 1) 7x * 2 + 7x * 1

Last update: November 28, 2019