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Factoring the Sum or Difference of Cubes - Problem 1

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Factoring trinomials. Now for this particular problem we are factoring x³ minus 8 which is the difference of cubes? If you think about it 8 is actually just 2³. So we need to go to our formula.

We have a formula for difference of cubes, a³ minus b³ is a minus b, the first sign is the same. 8² plus ab, the second sign is the opposite and then plus b², the last sign is always positive.

So from here we just want to plug in the corresponding a and b. So looking at this we have a³, x³, so a is just going to be x, a is 2³. So b is just going to be 2, and then plugging in the corresponding values. So this is just going to be equal replacing a with x and b with 2.

X minus 2, x² plus 2x plus 2² or 4. Using our formula our difference of cubes to factor x³ minus 8.

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