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Like terms are terms that contain the same variables raised to the same power. Only the numerical coefficients are different. 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.
all these terms have x^{2}y  
all these terms have xy^{2}  
this is the only x^{2}yz term  
this is the only xy term  
all these terms have x^{2}y^{2}  
this is the only xy^{2}z term 
Be careful when combining!
Terms like x^{2}yz and xy^{2}z 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!
Terms obey the associative property of multiplication  that is, xy and
yx are like terms, as are xy^{2 }^{and}^{
}y^{2}x.
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