Unit
Factoring
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!
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 a statement with only two terms; so there’s really only a few things we look for when we’re trying to factor a statement with two terms. They’re either going to be the difference of squares, or the sum or difference of cubes.
So looking at what I have behind me I have 8x³ minus 27. I know that 27 isn’t 8² so therefore I can rule out the difference of squares and I’m only left with sum or difference of cubes. Obviously we have a minus sign so obviously the only chance that this could be is the difference of cubes.
So the difference of cubes formula, hopefully you can remember is a³ minus b³ will factor to a minus b, the binomial of this sign agrees and then we’re left with a² plus the opposite sign ab and note there is no 2 here, it’s not like the one we’ were Foiling out a square where we have a 2 in there, just ab and then always plus b² at the end.
So really all we have to do for this problem is to figure out what our a is and what our b is. 27 is what cubed? 3, that’s pretty straight forward, so then we know that we are left with -3, +3, +9 and then all we have to do is to figure out what our a³ is. What cubed will give us 8x³? Obviously it has to be a single x and 8 is 2³, so therefore our a is just going to be 2x. Plug in your 2x in. 2x, 2x quantity squared is going to be 4x² and then this is a 2x in here and then plus 9.
This can be simplified to be 6x everything else still remains the same, so instead of rewriting everything, just imagine this is a 6x, and what we’ve done is factor the difference of cubes.