in this video you're gonna learn how to factor the sum and difference of two cubes so the first thing that you want to know are the formulas of course we're gonna go over that but you also want to know these perfect cubes these common ones that come up over and over again like 1 cubed is 1 & 2 cubed is 8 and 10 cubed is a thousand so see if you can memorize these that'll be helpful for recognizing when you have sum of two cubes or a difference of two cubes now the next thing we want to look at here is the formula and when you think about a perfect cube plus a perfect cube what you want to do is you want to take the cube root of this quantity you want to take the cube root of this quantity so you can figure out what your a and B values are and then we're go ahead and substitute in this formula as seen here now that acronym that a lot of students memorize when they're learning sum of two cubes in difference of two cubes is this soap acronym and what it stands for is same opposite always positive so if you're adding this is the same you're going to be adding then the next sign is going to be the opposite you're gonna be subtracting and the last one is always positive so that's just a nice way of remembering also when you do a difference of two cubes same thing when you're subtracting C it's the same you're subtracting then the opposite and then always positive so the only thing you really have to memorize then are a and B a squared a B and B squared it's the same for both formulas it's just that the signs are different so let's jump into these four examples and I'll show you how to work with these the first one x cubed minus 27 C if I take the cube root of x cubed C that's really gonna be like just axe so this is like our a value when I take the cube root of 27 that's 3 all right so this is going to be like our B value so we're subtracting so this is a difference of two cubes so we're gonna start off with X minus 3 so that's a minus B then x squared the opposite sign plus 8 times B which is 3 X always positive B squared so 3 times 3 which is 9 now a lot of students will say well Mario can't you factor this trinomial further and when you're doing these sum of two cubes in difference of two cubes this won't be able to be factored any further that's as far as we can go so this is your final result and you've got it factored now keep in mind when you're factoring you always want to look for that greatest common factor first if there isn't a greatest common factor then you can analyze is it a sum of two cubes difference of two cubes and proceed from there so let's look at a more difficult one now number two we've got eight y cubed plus one so what quantity times itself three times is eight Y cubed well that's going to be 2y times 2y times 2y and what times itself three times is one well that's just going to be one so sometimes people overlook one as a perfect cube now the reason I wrote it like this is just to identify the a value and the B value so a is 2y B is one we're adding so we're gonna want to use this formula here at the top and we're going to follow that soap acronym so we've got a plus B so this is the same we're adding we're adding then we've got a squared so 2i times 2y is 4y squared because this was adding we want to now do the opposite minus a times B which is 2y and the last is always going to be positive B squared so 1 times 1 which is 1 and now you've got it fully factored see if you can do number 3 and 4 we're gonna go through them together what time's itself is 64 d cubed well you can see 64 is 4 to the third power so this is really going to be 4 D 2 it's 4 D times 4 D or 40 cubed 125 is 5 cubed and so now this is going to be our a and our B in our formula so following that soap pattern that acronym we're going to say a minus B a squared which is 40 times 40 which is 16 d squared opposite since we subtracted here we're doing the opposite adding here a times B so for D times 5 is 20 D plus B squared which is 5 squared which is 25 remember the last one's always positive and that's it you've got it fully factored ok last example see if you can do this one 216 C cubed plus a thousand DQ this one what times itself three times is 216 well you can see that's going to be six cubed so this is going to be six see what times itself three times is a thousand well that's going to be ten cubed so this is going to be ten D the quantity cube so this is our a and this is our B so now if we put it all together we've got a plus B okay see this is adding so we're adding that's the same then we've got a squared which is going to be six C times six C that's 36 C squared and then the opposite so if we're adding we subtract that's going to be a times B that's 60 C D and the last one is always positive that's going to be e squared 10 D times 10 D which is a hundred d squared and you've got it fully factored if you want to see more examples of factoring specifically how to factor all different types I show you like a decision tree like how to decide what to do first second third follow me over to that really comprehensive video right there where I dive into all the different types I'll see you in that video