



If we have 3 pizzas and we go and get 2 more
pizzas we have 5 pizzas: 





3 Pizzas + 2
Pizzas = 5 Pizzas






Letters in math work the same way as pizzas. 


If we
have 3X and we go and get 2X more, we have 5X: 





3 X + 2 X = 5
X






Just think of the letter X like the word pizza. 


5
was the number of pizzas we had. 


5 is the number of X's we
have. 





We can do subtraction like this
too: 





6 X  2 X = 4
X



(Just like 6
pizzas  2 pizzas = 4 pizzas)






If somebody asked us you to add the number 6 and 3
pizzas, 


you really couldn't do it. Numbers and pizzas don't mix. 


The same
goes for trying to add stuff like: 





3 X +
2






We have 3 X's plus a silly 2. 


You can't add them
together. 





So 3X + 2 is just 3X + 2 











If we tried to add 3 pizzas and 4 bowling balls,



all we
would get is a big mess. 





You really can't add different stuff like
this together 


and get anything that makes sense. 


The same thing goes for
different letters. 


An X and a Y are as different as bowling balls and
pizzas. 


You just CAN'T add them together. 


So ... 





3 X + 4 Y
is just 3 X + 4 Y






Let's go back to stuff we can
combine. 


What could
we do with something like this: 





3 X + 4 Y + 2 X
 6 + 7 + 3Y






We have 2
different X things in that mess. 


We can
combine the two of them: 





3 X + 2 X = 5
X






Along with the rest of the glob we now
have: 





5 X + 4 Y  6 +
7 + 3Y






We can combine the Y's. 4Y + 3Y = 7Y. 


So we now
have: 





5 X + 7 Y  6 +
7






We can also combine the 6 and the
+7 





6 + 7 = 1 (Start at  6 and go up 7). 


That means
we now have. 





5 X + 7 Y +
1






Now, all the things that had the same letter (or
no letter) 


have been combined. 


That
means we're done. 





When two or more things have the same letter (or
no letter) 


we call them: 





LIKE
TERMS






A
Term
means any number, letter, or group of numbers and letters 


that are
separated from other things by a + or a . 





Like
means any term that has the same letter or letters. 


The same exponent on
the letter or letters. Or no letters at all. 





copyright 2005 Bruce Kirkpatrick 
