Combine Like Terms - Notes
Like terms are terms that contain the same variables raised to the same power. The coefficient (the number in front of the variable) can be different.
For example: 2xy, 6xy, -14yx are all like terms. They all have the same variables 'x' and 'y'. The coefficients ('2', '6', and '-14') can be different and will be used when combining like terms.
In an expression, only like terms can be combined. We combine like terms to shorten and simplify algebraic expressions, so we can work with them more easily. To combine like terms, we add the coefficients and keep the variables the same. We can't combine unlike terms because that's like trying to add apples and oranges!
Look at these 10 terms. Let's find all the like terms that can be combined.
  
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all these terms have x2y |
 
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all these terms have xy2 |
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this is the only x2yz term |
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this is the only xy term |
 
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all these terms have x2y2 |
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this is the only xy2z term |
Be careful when combining!
Terms like x2yz and xy2z look a lot alike, but they aren't and cannot be combined. Write the terms carefully when working out problems.
Don't overlook terms that are alike!
Look at terms carefully. The order of the variables can be changed and still be the same - that is, xy and yx are like terms, as are xy2 and y2x. Even though they are written in different orders, they still have the same variables and same exponents on those variables.