Distributive property versus order of operations

Added: 2026-05-17

[00:00:00]Hey everybody, I am here showing you guys a little bit of a difference. You can see that this problem is quite the same, almost looking, except for there's a slight difference in it and this is what's called distributive property up here and then this one is not distributive property and I'll explain why in a second. If you take a look at the top problem, the top problem has a -4 and then there's no symbol or any kind of operations in between that four number and the parentheses. So, when you have something like that, what you have is what's called distributive property. You're taking that -4 in this case and applying it to anything that's inside of the parentheses. Versus this problem down here, where you have the parentheses that you would solve, but then there is an operational sign after it. Now, we can still have a -4 and do distributive property if it's after that problem, but I'll show you what it would have to look like in order to make that happen. So, let's start by solving the first one on the top, where we're going to take the operations inside the parentheses first.

[00:01:00]Do that, which is 7 - 3, which is totally fine. You can do that and then we're going to have that -4 and so you see that that I'm going to just take that parentheses and I'm just going to reapply it inside of those parentheses with a positive four cuz that's what that outcome is going to be and then now I can do -4 * the positive four, which gives me a -16.

[00:01:21]Now, I could do distributive property after that, but what's going to look a little bit differently with this if I was to rearrange this and change it around to make that distributive property with a -4, I would have to write the 7 - 3 like this as you see down here, except for here, if it's after the fact, I would have to put that in parentheses because the way that this is written here, which is very slightly different, is showing me that once I've gotten the outcome right here, I'm then going to subtract four from it. This one is saying that I'm multiplying whatever the outcome of inside the parentheses is. So, this is the exact same thing as this. It's just written a little bit differently where the -4 is after that, which is something that you can totally do. Distributive property can be before or after the parentheses. You just have to be careful about how it's written when you see it. So, this would still give you that same outcome of a -16 because that parentheses is outside of that negative and the four. And then here, this is different because you have 7 - 3, which is four as well. But here, there's a minus four here. So, then it's 4 - 4, which is zero. So, there is your biggest difference between this problem and this problem and either of those two problems. And that's how the distributive property will work. And if you want more questions like these, you can find them on my YouTube, Instagram, and TikTok at youwonalgebra. These are going to be located in the distributive property playlist. Don't forget to share, like, follow for more, save this for later, and I will see you soon.