Combining Like-Terms

In this lesson we will discuss what like-terms are and how to correctly solve problems involving this topic. Like-terms are terms that have the same variable. These terms can be combined by adding or subtracting the coefficients. 

Example: 2y + 6y = (2+6)y = 8y 

In the example listed above both terms have the variable “y”. The coefficients 2 and 6 are added together to combine the terms. 

Example 1: 5y + 2y – 3x – 4x 

First, we should determine what terms can be combined. 5y and 2y can be combined because they have the same variable “y”. -3x and -4x can also be combined because they share x as a variable. 

The final answer should be reported in expression form: 7y-7x 

Example 2: -2y -3x +2x 

Determine what terms can be combined and report the final answer:

-2y -x 

Example 3: 2y -3(5y-2x) 

Before we can determine what terms can be combined, we must conduct some mathematical manipulation (distribution) in order to clearly see what terms can be combined. 

2y-3(5y-2x) = 2y – 15y + 6x

Now we can combine the two “y” variables and bring down the x term. The final answer should be reported as: 

-13y + 6x 

Example 4: 7(2m-2) + 2(m-5) = 

First distribute and the combine like-terms:  

7(2m-2) + 2(m-5) = 14m – 14 + 2m – 10 

Combine like-terms: 

14m – 14 + 2m – 10 

The final answer should be reported as:

16m – 24 

Example 5: 7a +3 (2-4a) 

Distribute first: 

7a + 3(2 – 4a) = 7a + 6 – 12a 

Now combine like-terms:

7a + 6 – 12a 

Report the final answer: 

-5a + 6 

Example 6: 7a – 2a 

Combine like-terms and report the final answer: 

5a 

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