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!

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Factoring the Sum or Difference of Cubes - Problem 1

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!

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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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