When I was quite younger, one of my hobbies was joining internet forums (fora?) on problem solving. I was not really good at it, so my role was only to ask questions. One of the internet forums I joined was the Art of Problem Solving math forum.
Art of Problem Solving (AOPS) is a community of problem solvers dedicated for math competitions – probably the best place on the web to ask hard (and very hard) math questions. One of the tricks I learned there was Simon’s Favorite Factoring Trick (SFFT), a factorization technique popularized by one AOPS member. The general strategy (see example 3) of SFFT is to add a constant or variable to an expression to make it factorable. This strategy can also be named as “completing rectangle” in analogy with “completing the square.” » Read more