Memorize the following identity

Hello there
I would like to hear the opinions of the members of this forum on the mnemonics methods employed on the memorization of math identities and formulae, more specifically the following identity:

x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)

I´ve seen many people saying that you should try to understand what the expression is saying before just memorizing it, and I agree with them but sometimes the relations are way too abstract and not intuitive at all like the identity above.

Maybe there IS a method to make it all intuitive and properly remember it without having to rely on pure rote learning, if so, please leave a comment on it.


The simple way is to make images for all the terms like x, z, +, =, ³, and so on. You can store it in a palace and have to make sure the images in the story appear in the same way as the equation. Even though this is simple, it is more tedious because of the amount of images you would have and how you would connect them.

The complex way is to make a symbol system for math which would reduce the amount of images you have. y³ would have an image instead of having just y and ³. YOu can even decide if you have + or - then your image looks a specific way. (x + y + z) could just be one image. The great thing about math is that you will have a lot of repreats of things being added or subtracted. Even the powers too.

Thank you for the reply

Do you have any examples of how such systems may look like?

It would be a math symbol system. You would create images for stuff like this

y+x or x+y (same thing)
x³ + y³
x³ + x
x³ - y³

So each one of those would have an image to them. So in the beginning it might seem like a bit of work to have the combinations of common terms you might see but if you are going to be dealing with math for a while, then if might be worth investing time in. You can see this like a double digit system. Creating images for every single symbol is like the single digit system. But once you combine terms, you can memorize more symbols with less images just like the double digit system.

I kinda like the idea of making image and then making a story that will help recreating the equation. :face_with_monocle:

I have done this when I needed to memorize equations!