Today in algebra II, we were learning to solve polynomial equations by factoring. When factoring a sum or difference of two cubes, I begin with the formal patterns and then I give my students a mnemonic to help them remember the pattern. I tell my students to remember how to factor the sum or difference of two cubes, just remember the word SOFAS.
For example to factor x^3 + 125, we get our binomial factor of (x + 5) and then we use SOFAS
S (Square the front) x^2
O (opposite sign) x^2 -
F (Front times back) x^2 - 5x
A (Always Positive) x^2 - 5x +
S (Square the Back) x^2 - 5x + 25
Answer: (x + 5)(x^2 - 5x + 25)
To help the students remember SOFAS, we draw a little poster with a picture of a sofa and then write out an example showing how to use SOFA. I know this little activity helps them, because the Precal teacher told me at the beginning of the school year that my students from last year taught her this and she was so excited that they actually remembered something from the previous year.