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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

When you are using algebra to solve your problems, one of your biggest and most often used methods is that of collecting like terms. Watch this video lesson to see how it is done.

When you are using algebra to solve your problems, one of your biggest and most often used methods is that of collecting like terms. But before we can talk about collecting like terms, we need to talk about like terms in general. What are they? **Like terms** are terms that share the same variable and exponent. You can also say that like terms are terms that like each other. Terms can be a single number, a variable, or a combination of numbers and variables multiplied with each other. If you think of the variable and exponent part of a term as the term's last name, then like terms are those terms that share the same last name and are thus part of the same family. If a term didn't have a variable attached to it, then that means it doesn't have a last name and is, therefore, related to all the other terms without last names, without variables attached. For example, 4*x*, 7*x*, and *x* are all like terms because they all share the same variables with the same exponents. 5*x*^2, 6*x*^2, 3*x*^2 are also all like terms. But, 4*x* and 3*x*^2 are not like terms. Why is this? Even though their variables are the same, their exponents are not the same. Yes, for them to be like terms, both the variables and the exponents must match.

If you saw a group of terms together, you would be able to identify like terms by looking at the variables and exponents of each term. This is the first step of collecting like terms on one side of an equation. Say, for example, we are trying to simplify the equation 4*x* + 5 + 3*x* - 2 = 0. If you see a problem asking you to simplify, remember that what it wants is for you to collect like terms together. To do this, we need to first identify which terms are like terms. What I recommend doing is to highlight the various like terms with different colors. I begin by highlighting the 4*x*. I continue reading my equation to see if there are other terms that are like 4*x*. I see a 3*x* with the same variable and exponent. That means that 3*x* is a like term to 4*x*. They both share the same last name of *x*. I keep reading the equation to see if there are more. Nope, that's it. Now I choose a different color highlighter, and I highlight the 5. I keep reading the equation to see if there are more terms that are like 5. Since I've already highlighted some terms, I can concentrate on reading only those terms that haven't been highlighted. Notice how I've included the negative. That negative tells me that the 2 is negative. It's very important to keep the right signs for the next step. I can go on to the next step now that I've highlighted all the terms on the one side of the equation.

The next step is to combine these like terms. So I look at my first highlight, and I notice that is a blue color. So I look for all the terms that are also highlighted in blue. I see, in addition to my 4*x*, a 3*x*. Combining these involves adding the number part together. So 4*x* + 3*x* = 7*x*. Now I need to add the rest. My next color highlight is purple. I see a 5 and a -2. Combining these I get 5 - 2 = 3. Do you see how important the negative sign is here? If we didn't pay attention to it and added the 2 instead of subtracting, our answer would be wrong.

Now that I've added all my like terms, I now need to write these in place of my like terms in my equation. To help me do this, I can rewrite my beginning equation so that the like terms are grouped together. So 4*x* + 5 + 3*x* - 2 = 0 becomes 4*x* + 3*x* + 5 - 2 = 0. I can replace the 4*x* + 3*x* with the 7*x*, and I can replace the 5 - 2 with a 3. So now my simplified equation is 7*x* + 3 = 0, and I am done collecting like terms.

Let's go over another example. Say the problem wants us to collect like terms for the equation 5*x*^2 + 8*x*^2 + 4*x*^2 + 1 = 0. How do we begin? We begin by first highlighting the 5*x*^2 using one color, say yellow. I continue reading the equation to see if there are other like terms to 5*x*^2. I see an 8*x*^2 and a 4*x*^2, so I highlight those the same color, yellow. Now I choose a different color, say pink, and I highlight the 1. I look at my equation and see that I've highlighted all my terms, so now I can go ahead and combine my like terms. Looking at my highlights, I see I have a group of 5*x*^2, 8*x*^2, and 4*x*^2 and I have a group of 1. The group of 1 is already combined, so I can leave that alone. Combining the group of 5*x*^2, 8*x*^2, and 4*x*^2 gives me 17*x*^2. Rewriting my equation with my combined like terms I get 17*x*^2 + 1 = 0, and I am done.

What have we learned? We've learned that **like terms** are terms that share the same variable and exponent. Terms can be a single number, a variable, or a combination of numbers and variables multiplied with each other. To identify like terms, we compare to see if the variable and exponent part of a term is identical to that of another term. To combine them, we add up the number part of each like term. To finish simplifying our equation, we rewrite the equation with our combined like terms in place of the individual terms.

Study this video lesson's information and prepare to:

- Characterize like terms
- Remember to use different colors to highlight like terms
- Combine like terms to simplify an equation

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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions 5:50
- Understanding and Evaluating Math Formulas 7:08
- Expressing Relationships as Algebraic Expressions 5:12
- Evaluating Simple Algebraic Expressions 7:27
- Combining Like Terms in Algebraic Expressions 7:04
- Practice Simplifying Algebraic Expressions 8:27
- Negative Signs and Simplifying Algebraic Expressions 9:38
- Writing Equations with Inequalities: Open Sentences and True/False Statements 4:22
- Common Algebraic Equations: Linear, Quadratic, Polynomial, and More 7:28
- Defining, Translating, & Solving One-Step Equations 6:15
- Solving Equations Using the Addition Principle 5:20
- Solving Equations Using the Multiplication Principle 4:03
- Solving Equations Using Both Addition and Multiplication Principles 6:21
- Collecting Like Terms On One Side of an Equation 6:28
- Solving Equations with Infinite Solutions or No Solutions 4:45
- Translating Words to Algebraic Expressions 6:31
- How to Solve One-Step Algebra Equations in Word Problems 5:05
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- How to Solve Multi-Step Algebra Equations in Word Problems 6:16
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