Math mistakes I make (frequently)

On previous posts, I’ve alluded to “dumb” math mistakes. Today’s practicing reminded me of them, again. I’m pretty sure the following one is my favorite so far:

Context: Barron’s review section on polynomials, Question #5: c^2 + d^2 = 4 & (c-d)^2 = 2.  After successfully factoring out and manipulating my equations, I had: -2cd = -2, which I blithely solved as cd = 2.  That’s right, apparently -2/-2 = 2 in my math world! While I’ve be working hard to catch these mistakes by re-checking my work, I’m still not getting everything.  Other than reading my questions and work out loud (which will clearly work come testing day), I’m still looking for brilliant ideas to check my work. Suggestions welcome!