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Binary expression tree

Posted on: June 28th, 2013 by
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Is there any way to algorithmically determine if two algebraic expressions are equivalent? For example is 5+x equal to x+5? Or how will a computer know (a+b)^2=a^2+2ab+b^2? Does the figure below give you a hint?
Binary tree

Brought to my attention by Shaleen. The original question can be found on Stack Overflow.

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