Next we'll look at how we use the distributive property with combining like terms to simplify expressions. This expression has a few things going on. We have seven being multiplied by a minus four in parentheses. And then as a separate term, we have plus three A. So where do we begin when we’re simplifying expressions? To know where to start, we think of the order of operations which tell us to first simplify what's inside parentheses. Well, here we have A minus four that can't be simplified any more than it already is, A and four are not like terms, so we can't combine them. So let's move on to the next step exponents. Well, there are no exponents in this expression, so we can keep going. Next, we move on to multiplication and division. We do have some multiplication. Here we have seven next to a set of parentheses. So that means the seven is being multiplied by what's inside the parentheses. We also have the multiplication with the three A that shows that three is being multiplied by A. But since three A is already as simplified as it can be, there's nothing we can do to simplify that term. But our first term, the seven times A minus four, that part can be simplified, but we have to use the distributive property. So remember, with distributive property, we're really just using multiplication. So that's why we can do it during our multiplication step of the order of operations. Wwe take the number that's on the outside of the parentheses and multiply it by each thing on the inside. So first we'll start by multiplying seven times A, which we can just write as seven A. Now we multiply seven times or minus four, which gives us -28, so that first part just becomes 7A -28. Now we can't forget our plus three A. So we'll just bring that on down. Now we're left with just addition and subtraction. So let's see how we can simplify this. Now, remember, when we're adding and subtracting, we can only add and subtract like terms together. Okay, so this is what we call combining like terms. This is done during the addition and subtraction step of the order of operations. Let's see what like terms we have. Here we have seven A and plus three A. They're like terms because they have the same variable, the A. So all we have to do is add seven A and three A together. Well, that gives us ten A and then we bring down the -28. There's nothing else to combine that with. So it just stays as it is. So our final answer is 10A -28. So look at what we just did. We took that whole big long expression that we started with. And just by using distributive property and combining like terms, we simplified it to just 10A -28. Here's another example. This time we have eight B and then minus six times B plus five in parentheses. Just like before, we can't start with simplifying what's inside the parentheses because B plus five can't be simplified any more than it is. We can't add those together. So we're going to have to rely on our distributive property and combining like terms to help us simplify it. Now, remember, when we use distributive property we’re not breaking the rules of the order of operations, we're still following the proper order. It's just that now, since we have some variables in here, we have to use these specific methods. Okay, so the distributive property gets done first before combining like terms because we always have to do multiplication before we add and subtract. So we're still following the proper order. So let's apply the distributed property. So we have a six in front of or to the left of the b plus five in parentheses. But we also have a subtraction sign to the left of the six. Remember, you always keep the sign that's to the left of the number or variable with it. That's the only way you'll remember if you need to treat it as a positive or negative. So since we have a subtraction sign with the six, we treat it as a negative six. So we're going to multiply that negative six times B, which becomes negative six B. We just smush them together, and then we have negative six times positive five. Negative six times positive five gives us negative 30. So remember those rules with integers? Multiplying a negative times a positive gives us a negative. So that’s negative 30. So far, that part of our expression simplifies to -6B -30. And don't forget we have that eight B that's in the front there. Let's bring that on down. So now we just have subtraction left to simplify. And that we can do by combining like terms. We have two terms that have the variable B, eight B and minus six B. We have eight of B and take away six of those, we're left with two of B, so 2B. And then we just bring down our -30 because there was nothing else left to combine it with. So all of that simplifies to just 2B -30. So very, very important to remember when you see subtraction or negative signs, slow down and take your time. For example, you have to remember that that subtraction sign stays with that six that we started with. So we treat it as a negative six. Okay, if you do that you'll make sure that your answer is correct with those positives and negatives. So to simplify expressions that have variables we still follow the order of operations, but we have to use the new methods that we've learned. So first we'll apply the distributive property which is the multiplication step of the order of operations. And then we can combine like terms, which is the addition and subtraction step. So just remember, distributive property first, and then you can combine like terms and you'll be able to simplify those expressions that have variables.