Probably the best advice is to read and work through a good book on Mathematica programming. Here is a good recent one:

http://www.amazon.com/Programming-Mathematica-Introduction-Paul-Wellin/dp/1107009464/

And this thread on Mathematica Stackexchange is relevant (and I really need to read it sometime)--there are some very clever folks who post there:

http://wolfr.am/1BW8o6x

Hello, every one.

Do you know how to compare 2 different functions in Mathematica?

For example how can I review that

(1 + x)^2 = x^2 + 2 x + 1?

Thank you.

I just bought this book on amazon: The student's introduction to MATHEMATICA by B. Torrence. Seams to me that is good enough but also seams a little old because it refers to Mathematica 5 and 7. I hope that I don't miss too much. My primary goal is to use Mathematica in my course of Calculus II for the next semester. In my University here in Mexico do not promote its usage but I think we are loosing too much with that decision. I also have the Maple 17 software and seams ok as a Calculus I and II companion. If you have any idea or guidance I will be very thankful. Thank you for your posts. Best regards.