How to judge whether equation satisfy or not programmatically?

Question

We all know this is true:

(a+b)c = ca+b*c

But how to judge it in programme?

Answer 1

http://en.wikipedia.org/wiki/Computer_algebra_system

Answer 2

One way is to convert the algebraic expressions in the same format.
Simplify both left and right expressions by applying the algrebraic rules.
For simple equations it won't be too hard to implement it.

Check out Simplify any Algebraic Expression. Tryout various expressions to get an idea.