Distributive Multiply Across

import mathy_core.rules.distributive_multiply_across

The Distributive Property can distribute multiplication across 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	✔

API¶

DistributiveMultiplyRule¶

DistributiveMultiplyRule(self, args, kwargs)

Distributive Property a(b + c) = ab + ac

The distributive property can be used to expand out expressions to allow for simplification, as well as to factor out common properties of terms.

Distribute across a group

This handles the a(b + c) conversion of the distributive property, which distributes a across both b and c.

note: this is useful because it takes a complex Multiply expression and replaces it with two simpler ones. This can expose terms that can be combined for further expression simplification.

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