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### Course: Pre-algebra>Unit 6

Lesson 9: Combining like terms

# Combining like terms

In this lesson, we learned how to add and subtract variables, like apples (a) or x's. We discovered that when we combine or take away the same variable, we can simply count them up or down. For example, 5x minus 2x equals 3x. This helps us understand basic algebra concepts. Created by Sal Khan.

## Want to join the conversation?

• Are you asking about how Sal said that the variable a can represent anything? What Sal meant was that if their is a question like 7b + 4b the variable b would not have to represent a specific object that begins with b. A certain amount of boxes could be the variable n. Also in a problem (lets say 6c + 2c) if the same variable is used that means its the same object. 6c & 2c both represent the same object. Hope this helped!
• We are studying problems that say name the like terms, -x to the 4th the power, 2x to the 3rd power, -5x the 4th power, -8x to the 2nd power, -6x to the 2nd power, -7x the third power and we are given options to choose from. I don't understand what they are asking. Am I supposed to combine like terms?
• Crystal.
When typing exponents, you can use the symbol "^" to mean "raised to the power of" So your equation can be written as
-x^4 + 2x^3 - 5x^4 - 8x^2 - 6x^2 -7x^3
To combine like terms, you want to first reorder the terms so the powers are from highest to lowest.
-x^4 - 5x^4 -7x^3 + 2x^3 - 8x^2 - 6x^2
The like terms can be combined. That is, the terms with the same power can be combined. I'll write it with parenthesis first to show which ones can be combined.
(-1x^4 - 5x^4) + (-7x^3 + 2x^3) + (- 8x^2 - 6x^2)
which when the like terms are combined becomes
- 6x^4 - 5x^3 - 14x^2

• Why do you do it this way? Basically if you think of 3x + 4x, you add the coefficients to get 7x. The idea behind this strategy is:

3x = x + x + x
4x = x + x + x

Think of x as the number of x-rays printed. Now, count the total number of x-rays: x + x + x + x + x + x + x
That's right! 7x.

Now think of 4f + 4g. f is fruit and g is grain. Grain and fruit are different, and no values are provided so it is not possible to make such conclusions in this expression.
• ok so what happens if a question like this occurs : 3a + 9b = ?

Would it be 12ab?
• Unless they ask you to do a specific formula like substitution or elimination, that should be right.
• So 100 + 100 + 100c + 100c = 200 + 200c?
• how could I answer something like -6(3+4x) Id really love a response quick since I have a test and I'm barely prepared! D:
• what about when the second number is just a variable like
4a+a=
• Well, when any variable is by itself, imagine a one in front of it, because it is 1a. 4a = 4a and 1a = 1*a = a

The answer to 4a+a = 5a

Hope this helped!
• i didn't get points for this! and my teacher gave this "combining like terms to me and my friends what is wrong?
• combing like terms is adding a variables to the same letters
• what would 3a+4A-2a=

is is 5a? or a+4A