I did not get a 10-year ban because I did not tell them I had been in the United States illegally. They do not investigate. There are too many applications to be processed. Never, never tell them that you were illegal in the country. If your fingerprints have been recorded because of being arrested or whatever, then they'll find out about your previous stay in the US. If you want to cross legally into the country from Mexico, always paint yourself as a good Mexican citizen that wants to spend money and behave well. Show them you have money in the bank, show them you want to return to Mexico upon finishing your travel. That is what immigration likes. Remember that.