Demontrer le resultat suivant " la difference des carres de deux nombres entiers consecutifs est egale a la somme de ces deux nombres "

     Since they are consecutive, meaning that one is another added to a unit.


 
     Where: a>b

     Now, we must mathematizing the problem:


 
     Note that, the result was expected because we made "a^2-b^2" in order to give a positive number, since "a" and "b" are positive, then the sum of both should also give a positive number.

If you notice any mistake in English, please let me know, because I'm not native.