Now we're going to learn how to evaluate expressions with multiple variables. In our last video, we saw how we can evaluate expressions, but they only had one variable in them. These will have more than one. Evaluate five A plus seven B for A equals negative six and B equals two. First let's write down our expression five A plus seven B. Now remember, when you have a number right next to the variable, it's the coefficient of that variable. In other words, we're multiplying that number times the variable. So our five A means that five is being multiplied by A, and seven B means seven is being multiplied by B. So we'll need to remember that when we plug those numbers in for A and B. So we're told that A equals negative six and B is equal to two. So let's substitute those numbers in for their variables. And we're going to use parentheses to show that we are using multiplication. So we have five times negative six, and it's in parentheses to show that five is being multiplied by negative six plus seven times two. And we can see how we plug those numbers in for the variables. Now we have an expression with just numbers in it, so we can use the order of operations to simplify it. So what operations do we have? We have multiplication and we also have addition. Remember, multiplication gets done first. So we're going to multiply the five times negative six, which gives us negative 30. And then we have seven times two, which is 14. So we bring down plus 14, negative 30 plus 14. And now all we need to do is the addition. Negative 30 plus 14 is equal to negative 16. So you can see we start with our expression, substitute the numbers in for their variables and then follow the order of operations to simplify it. Let's do one more. So now we have evaluate y squared, minus and in parentheses z plus seven for Y equals three and Z equals five. So let's jot down our expression and notice that we have the number two that's written up high as a superscript. That tells us that we have an exponent. So for that Y squared, we'll have to keep in mind that that will get simplified during our exponent step. And then we have minus, and then we have in the parentheses z plus seven. So let's take a look at what we numbers we need to substitute for the Y and the Z. We're told that Y is equal to three and z is equal to five. So let's plug those in. Now our expression becomes three squared because the three got substituted for the Y and then minus and inside the parentheses, five plus seven, since the five was substituted for the Z. So now our expression is all numbers and we can follow the order of operations to simplify it. So let's see what steps we have here we know that we have an exponent because we have the three squared. We also have subtraction because we have a minus sign after the three squared. And then we have some things in parentheses. And even though we have addition in the parentheses, since that five plus seven is inside of the parentheses, that will get taken care of during the parentheses step, not as a separate addition step. So let's start with that. Since parentheses is our first step in the order of operations, so that five plus seven will become twelve. Now our expression is three squared minus twelve, and then our second step is to simplify the exponents, which is the three squared. And since three is raised to the second power, that means that we're going to multiply three times three, which gives us nine. And then we'll just bring down the minus twelve. And notice that we don't have to keep the parentheses around the twelve, because it's just the number twelve in the parentheses, there's nothing else going on in there. And now we can with our final step of subtraction the nine minus twelve, which leaves us with negative three. And that's our final answer. So now you've learned how to evaluate expressions that have more than one variable.