An Intro to Combining Like Terms | Simplifying Expressions by Combining Like Terms | Math with Mr. J

Learn how to simplify algebraic expressions by combining like terms with clear examples and strategies in this intro video by Math with Mr. J.

Key Takeaways

Like terms have the same variables raised to the same powers and can be combined by adding or subtracting coefficients.
Rearranging expressions to group like terms together can simplify the process of combining them.
Subtraction can be rewritten as adding the opposite to help identify terms clearly.
Combining like terms simplifies expressions without changing their value, reducing the number of terms.
Understanding coefficients, including implied ones, is essential for correctly combining terms.

What the video covers

Introduction to the concept of like terms as terms with the same variables to the same powers.
Explanation of combining like terms by adding or subtracting coefficients while keeping the variable part unchanged.
Example 1: Simplifying 9x + 3x to 12x by adding coefficients.
Example 2: Simplifying 8g + 7 + 5g + 2 by combining like terms and constants separately.
Example 3: Simplifying a more complex expression 6y² + 10y + 2y² + 3y + y by grouping like terms and using a strategy to rearrange terms.
Example 4: Simplifying 7x + 2y - 4x + 2y by combining terms with attention to signs and rewriting subtraction as adding the opposite.
Strategies for organizing expressions to make combining like terms easier, such as rewriting expressions with only addition.
Emphasis on understanding coefficients, including the implied coefficient of one when none is written.
Demonstration that simplifying expressions by combining like terms does not change their value but makes them easier to work with.
Encouragement and closing remarks from the instructor.

Chapters

What are like terms in algebra?

Like terms are terms that have the same variables raised to the same powers. For example, 9x and 3x are like terms because both have the variable x to the power of one.

How do you combine like terms?

To combine like terms, you add or subtract their coefficients while keeping the variable part unchanged. For example, 9x + 3x becomes 12x by adding 9 and 3.

Why rewrite subtraction as adding the opposite when simplifying expressions?

Rewriting subtraction as adding the opposite helps to organize the expression so all terms are separated by addition. This makes it easier to identify and combine like terms, especially negative ones.

Full Transcript — Download SRT & Markdown

Speaker A

[Music] Welcome to Math with Mr. J. In this video, I'm going to go through an introduction to combining like terms. Now, remember, like terms are terms with the same variables to the same powers. When we combine like terms, we look for any like terms in the given algebraic expression and combine them into one term. By combining like terms, we can simplify expressions. That just means we can rewrite the original expression in a simpler and easier way to understand and work with. Let's jump into number one.

Speaker A

Where we have 9x + 3x. We will start with this basic expression and work our way up. So, we have two terms in this expression: 9x and 3x. Both terms have the same variable of x, and these variables of x are to the same power. Remember, when we don't have an exponent attached to a variable, there is an understood exponent of one. Anything to the power of one is just itself. So, 9x and 3x are like terms. Now, when we combine like terms, all we need to do is add or subtract the

Speaker A

coefficients, the numbers in front of the variables. The coefficients in number one are 9 and 3. We have a positive 9x plus a positive 3x, so let's add those coefficients. 9 + 3 is 12, and then we have the variable of x, and that's it. We took those two like terms, 9x and 3x, and combined them into one term, 12x. 12x is equivalent to 9x + 3x, so we didn't change the value of the expression. So, 12x is our final simplified expression. Let's move on to number two, where we

Speaker A

have 8g + 7 + 5g + 2. Are there any like terms that we can combine in order to simplify this expression? Yes, we have 8g and 5g. Both of those terms have that variable of g, and then we have constant terms 7 and 2. I'll box in the constant terms to separate them from the 8g and the 5g. Now, we can combine like terms. We have 8g + 5g, that gives us 13g, and then we have 7 + 2, that gives us 9. So, we end up with 13g + 9, and that's our simplified expression. That expression of 13g + 9 is equivalent to

Speaker A

the original expression. We were just able to simplify the original expression by combining like terms. We started with four total terms, but we were able to combine like terms, and now we only have two total terms. Let's move on to number three, where we have 6y² + 10y + 2y² + 3y + y. Let's find any like terms that we can combine. We'll start with 6y². 2y² is a like term. Both of those terms have that variable of y to the power of 2. Now, do we have any other like terms

Speaker A

within this algebraic expression that we can combine? Yes, 10y, and I will box these terms in order to separate them from the y squared terms: 3y and then y. Now, I do want to mention this term right here, the y, the variable by itself. The coefficient is one. We don't have a coefficient written in front. Whenever you see that, the coefficient is one. There is an understood one in front of a variable, and it can be helpful to write that one in there when you combine like terms, so you can always

Speaker A

write that one if you would like. Now, since this algebraic expression has five terms and we are working our way up to more complicated algebraic expressions, we're going to use a strategy to help us organize the expression before we combine like terms. We are going to rearrange and rewrite the expression and put the like terms next to each other. I'll start with 6y² plus the like term of 2y² plus now we have the y terms, so 10y + 3y + 1y. So, now all of the like terms

Speaker A

are next to each other, and it's a little easier to see what we can combine. So, this is a strategy to keep in mind. Now, do you have to do this step in order to combine like terms? No, but it can be helpful. Now, we can combine like terms. We will start with 6y² + 2y², so add the coefficients. 6 + 2 is 8, and then we have y². Plus, now we can combine the y terms, so we have 10 + 3 + 1. 10 + 3 is 13 + 1 is 14, so we get 8y² + 14y, and that's the simplified expression. We now have an

Speaker A

equivalent expression that is simpler than the original. We simplified the expression. We went from five terms to two terms. Let's move on to number four, where we have 7x + 2y - 4x + 2y. Let's find any like terms that we can combine. We will start with 7x and -4x. Now, when we combine like terms, a term is going to take the sign that's in front of it, so this is -4x. Then we have 2y and 2y, so let's box those terms in order to separate them from the x terms. Now, we can rewrite this

Speaker A

expression with the like terms next to each other. We will start with 7x - 4x, so we have a -4x there. Make sure to bring the sign that's in front of the term with it when we rewrite the expression. Plus 2y, so now we have the y terms plus another 2y. Now, we can combine like terms, so we have 7x - 4x, or you can think of this as 7x being combined with -4x, however you want to think about it. 7 - 4 is 3, and then we have the x, or if you're thinking about it as 7x combined

Speaker A

with a negative 4x, 7 and -4 give us 3 as well. Then we have our 2y + 2y, that gives us plus 4y, so we end up with 3x + 4y, and that's our simplified expression. We went from four total terms to two total terms by combining like terms. 3x + 4y is equivalent to the original expression. We were just able to, again, simplify this expression by combining like terms. Now, I also want to go through simplifying this expression a slightly different way to start off, and that's by rewriting the original

Speaker A

expression with only addition separating the terms. We do this by changing any subtraction to adding the opposite. The benefit of having all terms separated only by addition is that it's a little simpler to identify all of the terms, especially any negative terms. It kind of organizes the expression and helps any negatives stand out. I'll rewrite the expression off to the side here, so 7x + 2y - 4x + 2y. So, let's rewrite subtraction as adding the opposite. So, adding the opposite of a positive 4x is

Speaker A

a negative 4x. So, adding the opposite, let's rewrite the expression with that change. So, we have 7x + 2y + -4x + 2y. Let's rewrite that expression with like terms next to each other, so 7x + -4x + 2y + 2y. Now, we can combine like terms. We have 7x + -4x, that gives us 3x, and then we have 2y + 2y, so that gives us plus 4y. 3x + 4y that way as well. So, that's just another strategy to be aware of. So, there you have it. There's an introduction to combining like terms. I hope that helped. Thanks so much for

Speaker A

watching. Until next time, peace.

Topics:combining like termssimplifying expressionsalgebra basicsmath tutorialalgebraic expressionscoefficientsvariablesMath with Mr. Jalgebra strategiessimplify algebra

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