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High School Algebra I: Help and Review25 chapters | 292 lessons

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Lesson Transcript

Instructor:
*Jennifer Beddoe*

Combining like terms is a mathematical process used to simplify an expression or to add or subtract polynomials. Learn how to recognize like terms and combine them in this lesson, then check your knowledge with a quiz.

A **term** is a mathematical item in an equation that can be a **constant** (only a number) or a **variable** (a combination of numbers and letters that possibly have exponents). The number portion of a variable is called the **coefficient**. Some examples of terms include:

- 3 (a constant)
- 2
*x*(a variable) - 5
*y*^2 (a variable) - 3
*x*2*y*^3 (a variable)

**Like terms** are terms that have the same variables and exponents. They do not have to have to be the same coefficients.

When you were first learning to add, the problems you solved might have looked something like this: 'Tim has three apples, and Jane has two apples. Together, how many apples do they have?'

As the problems got more complicated, they might have looked something like this: 'Tim has three apples and four oranges. Jane has two apples and six oranges. If they put all their fruit in one basket, how many apples and oranges do Tim and Jane have?'

When you solve this problem, you can't just randomly add things together without respect to their type. You also can't add them all together and then combine the word - like they have 15 'orpples' or 'appnges.' You have to add the apples (there are five total) and the oranges (ten total) separately in order to solve the problem correctly.

Combining like terms is just like the problem with the apples and oranges. You can only add (or subtract) terms that are the same. And you don't combine variables; they will not change.

Let's try combining some like terms.

These terms are like terms because they both only contain the variable *x* so they can be combined. If there isn't a number in front of the variable, it's understood to be 1.

1*x* + 4*x* = 5*x*

There are two variables here: *x* and *y*. So, just like with the apples and oranges, you can only combine *x* with *x* and *y* with *y*. Some people find it easier to rearrange the terms so that the like terms are next to each other. A word of caution for when you rearrange terms: if a term begins with a negative sign, don't forget to transfer the negative sign, too.

This problem can be rearranged to be: 3*x* - 2*x* + 6*y* + *y*. Then, by combining like terms, the answer is: *x* + 7*y*

Here's another example of combining like terms:

Sometimes, the process of combining like terms is only the first step in solving a problem. It 'cleans up' the problem or makes it easier to see what to do next. This example shows how combining like terms can make a problem easier to solve:

**Like terms** are mathematical terms that have the exact same variables and exponents, but they can have different coefficients. Combining like terms will simplify a math problem and is also the proper form for writing a polynomial. To combine like terms, just add the coefficients of each like term. Remember that if there is no coefficient, it is understood to be 1. And don't forget to take negative signs into account.

Proper study of this lesson on combining like terms could result in your ability to:

- Compare 'terms' and 'like terms'
- Combine like terms
- Solve equations that require the combining of like terms

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High School Algebra I: Help and Review25 chapters | 292 lessons

- Why Do We Distribute in Algebra? - Explanation & Examples 5:39
- Distributing First vs. Adding First: Differences & Examples 6:44
- Distributing Positive and Negative Signs 5:56
- Distributing Algebraic Expressions with Numbers and Variables 7:57
- Changing Negative Exponents to Fractions 6:24
- Working With Fractional Powers 6:38
- Distribution of More Than One Term in Algebra 6:12
- Combining Like Terms: Definition, Simplifying & Practice 4:06
- Go to High School Algebra - Algebraic Distribution: Help and Review

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