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Lesson 13: Combining like terms

# Combining like terms example

In this lesson, we learned how to simplify algebraic expressions by combining like terms. We focused on understanding the intuition behind adding and subtracting coefficients of the same variables. The result is a simplified expression, making it easier to work with and solve problems. Created by Sal Khan.

## Want to join the conversation?

• why is X the most common letter used in math?
• Can we actually combine terms like that? First, it was in the right order and then Sal changed the order to gather same species. But I don't know if ...
• Yes you can!
The mathematical property which allows us to do so is the commutative property of addition, which says, essentially, that, "when adding things up, order doesn't matter," so x+y+z=x+z+y=z+y+x etc.
So if I have 2x + 3y + 4z - x - 2y - 3z, I can rearrange that to 2x - x + 3y - 2y + 4z - 3z.
Then I can combine the like terms, shown with parenthesis: (2x - x) + (3y - 2y) + (4z - 3z)
2x - x = x
3y - 2y = y
4z - 3z = z
Now where there is the 2x - x I can replace that with x: x + (3y - 2y) + (4z - 3z)
Where there is the 3y - 2y I can replace that with y: x + y + (4z - 3z)
and finally the z terms to get x + y + z which is exactly equal to the original expression, that is:
2x + 3y + 4z - x - 2y - 3z = x + y + z.
• i don t get what minus one z from 8 z and it equals 7 how? this happens around to
• It's 8z - z. Think of it as 8 - 1. z is also just another way of saying 1z.
• how would , for example 2z-7-1 = 2z + 8
• if your are able to do it right you are able to have the variable a zero
• Okay now I've watched this and I'm still a little confused
• well you are just add the X's to the numbers like this (the first number is the coefficient btw)2x +4X = whatever the answer would be.
• so i'm confused with this question:

Combine the like terms to create an equivalent expression.
4t−t+2

and it said the answer is this:
4t-t+2=(4-1)t+2
= 3t+2

I am confused where did the (4-1) come from? I understand where the 4 is from but where did the 1 come from? I dont see any 1 inside the question
• Remember, a variable without a visible number in front has a coefficient of 1. So, your problem is actually:
4t-1t+2
Combine the 2 terms containing "t" by subtracting their coefficients and you get 3t+2

Hope this helps.
• when I watching this video this looks so easy but when I taking the test it's really hard!

like this one - 4q - ( - 8q) + 10

I thought the answer is - 12q + 10

bcoz the the rule is "negative minus negative" the number will be just get more negative?
• No, the number wont get more negative.
When there is an equation like this -4q - (-8q) +10, where there is a minus sign in front of the brackets, the sign(s) inside the brackets get changed. So the equation becomes this: -4q +8q +10.
• How do you Combine the like terms to create an equivalent expression? Like for example 4p +6 −3 how would you solve that?