We are now going to learn some special factoring formulas for binomials – Sum and Difference of Cubes.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
To factor the sum/difference of cubes, we use the Factoring Cubes Formula that will create the product of a binomial and a trinomial.
Sounds simple, right?
Factoring patterns for Sum and Difference of Cubes
Yes, it’s just as easy as factoring the Difference of Square.
All we have to do is follow the formula for factoring cubes, and away we go!
So what trips students up?
The signs!
There’s a lot to keep track of, and the signs are what causes the most mistakes. Then how do we keep everything straight?
We use a fun mnemonic device SOAP! which stands for Same Opposite Always Positive.
As Purple Math accurately states, the letters in the acronym help us to memorize the signs for each term in the formula. The linear factors in the factored binomial will have the “same” sign as the sign in the middle of the original expression. Then the first sign in the factored trinomial expression will have the “opposite” sign from what was in the original expression, and last the second sign in the factored trinomial expression is “always positive.”
Together we are going to factor 11 sum or difference of cubes, as well as perfect cubes.
Factoring Cubes (How-To) – Video
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