Terms, Variables, Coefficients & Constants | Parts of an Algebraic Expression

Welcome to Math with Mr. J. In this video, I'm going to cover terms, variables, coefficients, and constants, all very important parts of algebra. So understanding what these words mean, understanding the language, will set us up for success. We'll walk through what each of these are and go through a handful of examples. Let's jump into number one, where we have 5x plus 8. Now this is an algebraic expression. Let's identify the terms, variables, coefficients, and constants. We'll start with terms. Now a term is part of an expression, separated by addition or subtraction. A term can be a number, a variable, or a combination of both. So looking at 5x plus 8, we have two terms. We're looking for parts of this expression, separated by addition or subtraction. 5x is a term, and 8 is a term. Remember, a term can be a number, a variable, or a combination of both. So our terms are 5x and 8. Now keep in mind, a term takes the sign directly in front of it. Looking at our first term, 5x, there's no sign in front of it. That means it's positive. Then we have plus 8, so that's a positive 8. So our two terms, 5x and 8. Let's move on to variables. Now a variable is a symbol, usually a letter, used to represent a number. A variable can represent one specific number, or a number that changes, a number that varies. So in our expression here, do we have any variables? Do we have any letters? Yes, this x right here. So we have one variable, x. Next, let's move on to coefficients. A coefficient tells us how many times a variable is being multiplied. A coefficient is the number in front of a variable. So for our expression, we have one coefficient, this five right here in front of x. This tells us we have five x's, five times x. So again, we have one coefficient in this expression, five. Just remember, a coefficient is the number in front of a variable. Now sometimes we won't see a number in front of a variable. But we'll take a look at that in another example. Lastly, we have constants. A constant is a fixed number, a number that does not change. Think about the word constant. Constant means something stays the same. So the value of a constant in an expression stays constant, it stays the same. Basically, there's no variable attached to a constant to change its value. So a constant's value is locked in. Our constant in this expression is eight. And this is a positive eight. Constants take the sign that's in front of them. So again, this is positive. So there's an overview of terms, variables, coefficients, and constants. Let's move on to some more examples to really get this down. So taking a look at some more examples here, we have our expressions on the left. And we need to identify the terms, variables, coefficients, and constants for each. So jumping into number two here, let's start with the terms. The parts of the expression separated by addition or subtraction. Well, we have m and then minus seven. Remember, a term takes the sign in front. So we have two terms here, m and negative seven. So m and negative seven. Next, we have variables. Do we have any variables here? Yes, we have one, m. Now we have coefficients. And this is a very important example here. Remember, a coefficient tells us how many times a variable is being multiplied. It's the number in front of a variable. Now here, we don't have a number in front of m. So would our coefficient be zero? Well, do we have zero m's in this expression? No, we have one m, one of that variable. So whenever we just have a variable, there's one of that variable. So there's an unwritten one in front. It's understood there is one of the variable. So we can leave the one out. We don't need to write the one. And you may hear this called an implied one. So our coefficient here is one. One m is the same thing as just m. So again, whenever we just have a variable, there's one of that variable. So the coefficient is one. Lastly, we have constants. And for constants, we can think of it like looking for numbers that stand by themselves. For number two here, we have a seven. And remember, constants take the sign in front. So this is negative seven. Our constant here, negative seven. Let's move on to number three, where we have three x plus two y. So for our terms, we have three x and two y. And they are both positive here. So three x and two y. As far as our variables, we have two x and y. Next, we have coefficients. Well, we have three x. So three is a coefficient. And then two y. So two is a coefficient. We have two coefficients here. Three and two. And then for constants, we actually don't have any constants for this expression. And that's okay, that happens. An expression doesn't have to have a constant. So we'll put none here. Moving on to number four, we have negative four a minus b plus five. As far as terms, we have three for this expression. We have negative four a, negative b, and five. So we have negative four a, negative b, and five. Moving on to variables. Well, we have two variables here, a and b. Then for our coefficients, well, we have negative four a. So negative four is a coefficient. And then for b, we don't see a number in front, which we know that means we have one of that variable. There is an implied or understood one in front. But here, we need to consider the sign in front as well. So this is a negative one for our coefficient. We can think of this as negative one b. That's the same thing as just negative b. So our coefficients are negative four and negative one. And then as far as our constant here, that's going to be five. Lastly, for number five, we have 10x squared. Here, we actually just have one term. We don't have any addition or subtraction separating parts of the expression. 10x squared is the full expression. So we just have one term here, 10x squared. As far as variables, we have one. That's x. And then for our coefficient, the number in front of that variable, that's going to be 10. So our coefficient here is 10. And then lastly, do we have a constant? No, so we can put none. So there you have it. There's an explanation of terms, variables, coefficients, and constants. I hope that helped. Thanks so much for watching. Until next time, peace.