Factoring Cubes

Video Transcript

"So how does one factor cubes? Hi, I'm Jimmy Chang. I have been teaching college mathematics for nine years. And when it comes to factoring cubes or cube expressions. It might be a little intimidating. But once you see the pattern, it actually works out pretty well. So here's an example for you. Now suppose you want to factor X cubed plus eight. Now the first thing to do, is to make sure that both terms are written in terms of cubes. Now we know that X cubed is of course, already cubed. Now the question is, what number cubed is going to give you eight? In other words, what number multiplied by itself three times. Is going to give you the number eight? Well, after some thought, you'll come to the conclusion that eight is indeed two to the third power. Now when it comes to factoring. Basically, you want to break it up into two parenthesis. Like you normally would in regular factoring. So you have however, one twist. A smaller parenthesis and a larger parenthesis. The smaller parenthesis will have two terms. The larger parenthesis, three. Now you break them up proportionally. In other words, for X cubed, there's going to be a smaller part and a big part. For example, it will be X for the smaller. X squared in the larger parenthesis. Now for the two cubed, it'll be two and two squared. So as you can see, the smaller terms belong in the smaller parenthesis. And the larger going in the larger parenthesis. Now for the plus signs, two pluses normally make a plus. So that will go in here. But what about that third term? The third term in the larger parenthesis, is always going to be the two. The two terms in the smaller parenthesis multiplied together. In other words, X times 2. Well, that's going to give you 2X. And that will take it's place in the larger parenthesis. Also with cubes, with every factoring of cubes. There will always be one negative and two positive signs. Since I already have my two positive signs here. The negative sign is the only place to go in there. Now if I wanted to factor X cubed to minus 8. Same exact idea. The X will go here. X squared will go here. We know 8 is 2 cubed. Two goes here, two squared goes up there. For for negative signs. To get a negative sign, you have a negative and a positive. Well, because you already have your negative. You know, you need to positives. The positive sign has to go in there. As for the middle term, like we said before. If you multiply the two terms in the smaller parenthesis. You will always get your middle term. X times two is going to be 2X. Simplify the two squared and you'll be finished. So I'm Jimmy Chang. And that's a demonstration on how to factor cubes."