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Factoring the Sum or Difference of Cubes - Problem 1
University of Michigan
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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 xÂ³ minus 8 which is the difference of cubes? If you think about it 8 is actually just 2Â³. So we need to go to our formula.
We have a formula for difference of cubes, aÂ³ minus bÂ³ is a minus b, the first sign is the same. 8Â² plus ab, the second sign is the opposite and then plus bÂ², 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 aÂ³, xÂ³, so a is just going to be x, a is 2Â³. 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, xÂ² plus 2x plus 2Â² or 4. Using our formula our difference of cubes to factor xÂ³ minus 8.
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