We've learned how to simplify expressions by combining like terms. Next, we're going to learn another strategy for simplifying expressions, which is called using the distributive property. But before we actually apply it to different expressions, we're going to first make sure that we understand what it is and why it works. Let's start with this expression. We have three, and then in parentheses, we have four plus five. Remember when we have a number written right next to a set of parentheses that implies multiplication. So this three is being multiplied by what's in the parentheses, the four plus five. Let's review how we can solve this problem using the order of operation, PEMDAS. Okay, so the P in PEMDAS stands for parentheses. So we start by simplifying what's inside the parentheses, the four plus five, which of course gives us nine. So this problem becomes three times nine. And now we can use multiplication to simplify it even more. And three times nine gives us 27. And there we go. Our expression is fully simplified. Another way that we could solve the same problem is with using the distributive property. Now, the distributive property tells us that when we have a number outside of a set of parentheses, or it could also be a variable. But in this case, we just have the number three. That three can be multiplied by each term inside the parentheses as separate steps. So instead of first adding the four and five together, we can multiply the three times the four, which gives us twelve. And now we go back and multiply the three times the five as a separate step. And remember, include whatever sign, whatever symbol is to the left of the term, whether it's an addition or a subtraction sign, so you know whether to treat it as positive or negative. In this case, we have a plus five, so it's a positive five, and three times positive five gives us positive 15. Now we can add these together twelve and positive 15 gives us 27. Now, notice we ended up with the exact same answer both ways. So now you can see that there are two different ways to solve a problem like this. You could use the order of operations, but in some situations where order of operations might not work, you can also apply the distributive property. So let's review it. We use the distributive property when a number or variable is being multiplied by a group of terms that are inside parentheses. And to do this, we multiply whatever is on the outside by each term that's inside the parentheses. So if we have A being multiplied by B plus C inside the parentheses, multiply times B as one step, and as a second step, multiply A times C. So we could write this over as A times B plus A times C. So this is a way to represent the distributive property as a general formula with the variables A, B and C.