Distributive Property For Factoring (Let's Learn Factoring)

all right distributed property I know we still have not got to factoring but I'm telling you this is probably one of the most important lessons for I want you to be able to visualize what we're doing so you can start to see why it is we're trying to factor and what we are looking for I kind of forgot some parentheses here so what we need to do is remember the kind of two rules for distributive property if I have a * B plus C remember this a needs to multiply by the B and the C so this will be AB plus an AC and then furthermore yeah we'll get to that but what I want you to see here is factoring is basically the process of going from here to there right so we're going to practice going from here to here but what I want you to be able to see is once each and every time that I apply distributive property to each of these problems what I want you to see is look at the answer and kind of Look Backwards kind of Follow That procord backwards because that's where students get hung up with factoring when we get into the next lesson we're going to do factoring we're going to get right into it right and I have some lessons I have tons of example problems but I want you to be able to see where working forward practice or factoring is going to be the process of working backwards from the distributive property so in this first example I have 3 * x - 2 we're going to multiply 3 * X and 3 - 2 so therefore I have a 3X - a 6 and again remember what I said if I wanted to factor 3x - 6 what would that look like it would look like this three times an x - 2 we'll talk more about that later but I want you to be able to see again I have a monomial times a binomial need to multiply everything times everything remember numbers multiply by numbers variables multiply by variables so therefore this is going to be a 6 x^2 and a 2X * 5 I can only multiply the 5 * the 2 so that's going to be a positive 10x now we get into a trinomial I don't have anything for a trinomial here right but the distributive property still works ladies and gentlemen what we're simply going to do is multiply the four times everything and the x times everything you could also use foil you can use a foil phase there's a lot of techniques that we use to help students remember but this is about factoring so I'm hoping assuming that probably already know this I just want you to visualize what happens when we multiply binomial times a binomial that looks something like this CU there is something interesting about this it's the exact same numbers except one's negative and one is positive so4 * X is a -4x -4 * 4 is going to be a -16 x * X is going to be a x^2 and x * 4 is going to be a positive 4X so the one thing I want you to recognize here is when I go ahead and simplify this sorry that's a plus X squ when I go ahead and simplify this I can say well I have an x s right what about my x's Well - 4x and posi 4X those are going to add to zero so I don't have any X terms and then I have A6 that looks very similar to that example I showed you with those little boxes remember the x^2 minus one this is going to be an x squ - 16 what about a problem over here so again just follow the same steps now typically I always like to multiply the first two terms first that's going to be our foil so we do first so 2x * a 5x is going to be a 10 x^2 and then we do first outer so we do 2x * negative 1 which would be your outer terms 2x * 1 is going to be -2X then we do our inner -1 * 5x is going to be a 5x and then we do our last so we do inner last 1 * 1 is going to be a positive one now the big thing that happens to students and the reason why I had to spend some time doing this with you guys is because when I teach factoring or I make a video about how to do factoring it is like without a doubt students will always ask where' this number go what happened to that number like how' it just eliminate nothing is being eliminated ladies and gentlemen when I go and simplify this right the 4X and the 4X those added to zero right I didn't eliminate I just like poof and it's gone but then when I combine them when I simplifi them that is how I got the ZX or no middle term over here when I go to simplify this -2X minus a 5x is a -7x right so when you go to simplify there these are the only two terms that I can go ahead and simplify I can't combine everything with the 10x S I can't combine anything with the one these two terms though can simplify so my final answer is a 10 x^2 minus a 7 x + 1 and guess what we're going to learn how to factor from here to there sometimes you could do it in your head but this might be a little bit difficult but I want you to be able to see this is very very important because we're going to get to this so if I don't study if I don't teach it now then when I'm teaching factoring I have to go back to it and be like oh here's how this works notice a 10 x^2 - 7 x + 1 if I was to work my way backwards notice how 7x I can break that up into a -2X and a 5x then I can Factor things out it's just a very important concept of this idea of distributed property and factoring is just going to be the reverse of that now on the last one I threw in three terms because it's important for you to recognize when we need to disturb a property we want to work one thing at a time so I have a 2 * x -1 * x + 2 now thankfully multiplication is cative so it doesn't matter which one you do first I would just maybe recommend doing your two binomials first and then whatever scaler you have then to go and do that or whenever you have like three binomials if you know you're moving on something more advanced just pick two at a time and then multiply everything by the third one so I'm going to do two times now let's multiply this out X now I'm not going to show any lines here we're going to kind of pick it up x * X is an x^2 x * 2 is going to be a POS 2x- 1 * X is a x and - 1 * 2 is going to be a -2 now if there wasn't a video that was a little educational I would probably simplify that in my head and write it down but I don't know where you're at so that's why I'm going to work it in a little bit slower so x^2 let's see plus x - 2 now I can apply my distributive property so we're doing a lot of work here and that is going to give us a 2 x^2 + a 2x - A4 and what's reason what the reason why this is important that I want you to be able to see is when we're factoring one thing we're always trying to do is trying to say all right is there anything in common that all of my terms have that I can first factor that out and again when I say the word Factor I'm saying rewrite the expression as multiplication see what happens here I multiply the two times each and every one of these terms when I'm given this problem and I want to factor it what I'm basically doing is dividing each of these these terms by two because all of these terms share a common factor right remember first video they share a common factor of two because two is divisible into each and every one of these terms so if I divide out of two and rewrite it as multiplication I can rewrite it like this then I would have to go into my factoring techniques of trinomials notice how I broke up the X into a 2X and a Negative X and again how am I going to do that well we're going to learn that in the upcoming videos but I just want you to see this process or I want you to start visualizing the idea of what we're trying to achieve with factoring going from this term going in the reverse of the distributed property and guess what ladies and gentlemen it is now time to get in factoring on the next video