Factoring Cube Functions

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When factoring cubes, remember that the pattern is usually the same for both the sums and differences of the cubes. Find out how to work with parentheses when factoring cubes with help from a math teacher in this free video on basic math lessons.

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Video Transcript

So how do you factor cube functions? Hi, I'm Jimmy Chang and I've been teaching college mathematics for nine years. And by now you've probably learned how to factor square functions, the perfect square functions but how do you solve and factor cubes? Well, here's a demonstration on how you do that. And the pattern's the same for both sum and differences of the cubes, but with one little exception. But first things first. Here's an example. Suppose you wanted to factor x cubed plus twenty seven. Now what you have to think about first is write the two terms as cubes. Now, x cube is already a cube so you don't have to worry about that. However, with twenty seven, you have to think about it in terms of cubes. For example, what number cubed is twenty seven? In other words what number multiplied by itself three times will give you twenty seven. Well, after a little bit of thought you'll come to the conclusion that twenty seven is really three cubed. Now, here's how you factor it. You're going to need a smaller parenthesis and a larger parenthesis. Now, the smaller parenthesis will contain the smaller terms and the larger parenthesis will contain those larger terms. Now with x cubed you can break them up as a smaller part and a larger part. So, it'll be x and x squared. Now by the same token, you can split them with three cubed as a smaller and larger part. The three is going to go in the smaller parenthesis and the three squared is going to be in the larger parenthesis. Now, to get a plus sign you have two pluses that generally will give you a plus. So we're going to have two positive signs. Now you may have noticed that I left a gap on purpose for the larger parenthesis. Well that's because the larger parenthesis will always have three terms. Now, what is that third term going to be? Well, the third term is when you multiply the x and the three, which is going to be three x. Now something else about factoring cubes, you're always going to have two positives and one negative side. Now since we already have the two positives you will have the negative sign right here. Now what if you want to factor x cubed minus twenty seven? Here we go very quickly. You already know it's three cubed so it will be x cubed minus three cubed. Now just like the sum of two cubes, you also have two positive and one negative sign. So here we go. You will have x and x squared and three and three squared. Now to get a negative sign, generally you need a negative and a positive. But remember what I said about needing one negative and two positive signs? Since I already have my one negative, this has to be a positive. And the term that goes in here is x times three which is three x. So, my name is Jimmy Chang and that is how you factor cube functions.


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