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.

Addition

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