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What are like terms? How do you combine them? Can you give me an example for I know how to do it?

 Dec 18, 2014

Best Answer 

 #1
avatar+118608 
+10

like terms are terms that you are allowed to add or subtract together.  

They must have the same letter and those letters must be raised to the same powers.

It is easiest to think of the letters as things (just for add and subtract - doesn't work the same for mult or divide)

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ex

3C+8B-C+6d

you could think of this as

=3cats + 8bananas - a cat +6dogs

=3cats + 8bananas - 1cat +6dogs        (a cat is the same as 1 cat)

now the cats are like terms - I can put those together   (3cats)+(-1cat) = 2cats   

note that the minus sign always belongs to the term following it.

so now we have

=2cats + 8bananas +6dogs 

The other things are all different - they are unlike terms - so the simplification is finished.

=2C + 8B + 6D

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5mt + 8t - m +10tm + 2t^2m

The only terms here with exactly the same letters raised to exactly the same powers is 5mt and 10tm.

It doesn't matterthat the letters are in a different order because

10tm=10*t*m=10*m*t=10mt

5mt+10tm=15mt  (or    15tm)

so the answer is

15mt + 8t - m + 2t^2m

It cannot be simplified further because there are no more like terms.    

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 Dec 18, 2014
 #1
avatar+118608 
+10
Best Answer

like terms are terms that you are allowed to add or subtract together.  

They must have the same letter and those letters must be raised to the same powers.

It is easiest to think of the letters as things (just for add and subtract - doesn't work the same for mult or divide)

-------------------------------------------------------------------

ex

3C+8B-C+6d

you could think of this as

=3cats + 8bananas - a cat +6dogs

=3cats + 8bananas - 1cat +6dogs        (a cat is the same as 1 cat)

now the cats are like terms - I can put those together   (3cats)+(-1cat) = 2cats   

note that the minus sign always belongs to the term following it.

so now we have

=2cats + 8bananas +6dogs 

The other things are all different - they are unlike terms - so the simplification is finished.

=2C + 8B + 6D

------------------------------------------------------------

5mt + 8t - m +10tm + 2t^2m

The only terms here with exactly the same letters raised to exactly the same powers is 5mt and 10tm.

It doesn't matterthat the letters are in a different order because

10tm=10*t*m=10*m*t=10mt

5mt+10tm=15mt  (or    15tm)

so the answer is

15mt + 8t - m + 2t^2m

It cannot be simplified further because there are no more like terms.    

------------------------------------------------------------

Melody Dec 18, 2014
 #2
avatar+390 
+5

Okay thanks so much!

 Dec 18, 2014
 #3
avatar+7188 
+5

Very good answers guys....I haven't gotten to like terms in my Fundamentals of Geometry and Algebra course yet

 Dec 18, 2014

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