# Factoring algebraic expressions using the distributive property | Algebra I | Khan Academy

From the earlier math you already know, you probably know about the idea of \u200b\u200ba multiplier. For example, let me choose any number, the number 12. We could say that the number 12 is a product of two and six; two by six is \u200b\u200bequal to 12. Because you have the work of two and six and you get 12, we could say that two is the divisor of 12 and we could also say that six is \u200b\u200bthe divisor of 12. You have the product of these things and you get 12! You can even say that this is 12 in decomposed form. People don’t usually talk that way, but you can look at it that way. We broke 12 of the things we could multiply. And you probably remember from earlier math the notation for the decomposition of prime factors, where you decompose the number of all its prime factors. In this case, you can decompose six two and three, and you will have two by two by three is equal to 12. You will say, “Okay, this is going to be 12 in its decomposed form of prime factors or decomposition of 12 “, and these are the simple multipliers. The general idea, this concept multiplier refers to the things you can multiply one by one, to get the original thing. Or when we talk about the decomposed species, you essentially take the number and decompose it of things, in the multiplication of which you will get the original number. What we will do now is development of this idea in an algebraic definition set. If we start with an expression, let’s say the expression is two plus four x, can we decompose it into a work from two other numbers or two expressions, or the product of number and expression? One of the things you can think of is is that we can write this as two by one, plus two x. And if you want, you can check that this is really equal to two plus four x. We’ll just reveal the brackets. Two by one is two, two by two x is equal to four x, so is plus four x. In algebraic reasoning, this often will be considered or referred to this decomposed expression or in decomposed form. Sometimes people say that we put two in front of the brackets. You can easily say that one plus two x is in parentheses. And you have this broken down into two of its multipliers. Let’s solve a few examples and then think about it, which I just introduced you to, and how we actually find it. Let’s solve another example. Let’s say you have six, let’s just change the color, six x, six x plus three. No, let me write it as six x plus 30. That’s interesting. Let’s ask ourselves can we decompose each of these articles in such a way that that they have a common multiplier. This here, six x literally represents six by x, and then 30 if I want to export six, 30 is divisible by six, so I could write it like six by five, 30 is the same thing as six by five. And when you write it that way, you see you can take six outside. In essence, the opposite is true of the distributive property. I’m actually canceling the distribution property, I export six and I will get it in the end six by if I take six out here, I will have x and export from outside six here, I have plus five. So six x plus 30, if we decompose it, we can write it as six by x, plus five. And we can check it with the distributive property. If you divide that by six, you get six x plus five by six or six x plus 30. Let’s do something that is small more interesting where we would wanted to bring out the front of the liver. Let’s say that … Let me put a new color here. Let’s say we have 1/2 minus 3/2, minus 3/2 x. How can we write this in decomposed form, or if we want to export something? I recommend you pause the video and try to find it, and I’ll give you a hint. See if you can take 1/2 outside. Let’s write it this way. If we try to take 1/2 out, we can write this first article as 1/2 one, and this one the second to write as minus 1/2 for three x. It’s the same, 3/2 x is the same as three x divided by two, or 1/2 by three x. And then here we can see that we can just export outside 1/2 and we will get 1/2 one minus three x. Another way you can do this is to say: “Hey, look, both works include 1/2. “And that\’s a little more confusing, after you have to deal with the liver. But one way to look at it is that I can divide and export 1/2 of each of these articles. If I export 1/2 of this, 1/2 divided by 1/2 is one. And if I take 3/2 and divide it by 1/2, it will be three, so I export from outside 1/2, which is another way to do it. I don’t know if that confuses you more or less, but hopefully it gave you the idea of \u200b\u200bdecomposing an expression. I will solve another example where we even use even more abstract things, I can say “ax plus ay”. How would we write this in decomposed form? Both articles contain works from a, so I could write this as a, by x plus y. And sometimes I hear people say that I took out a. You can check it if you multiply it again. If you distribute a, you get ax plus ay.