Like terms are ones that have the same 'letter' part. When you combine them, you add/subtract the number parts. If there is no number, then a '1' is understood. It's like adding apples to apples and Oranges to oranges. Some examples:
5 apples + 3 apples = 8 apples
5x + 3x = 8x
7b-b+4b = 6b+4b = 10b (Notice that you work from left to right.)
5.2xy3z +3.96xy3z = 9.16xy3z
5g+7h+j-2k-g+10h+j-6k = (5g-g)+(7h+10h)+(j+j)+(-2k-6k) = 4g+17h+2j-8k. (Notice how the '-' on the 2k went inside the parentheses)
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To add like terms, find the terms that have the same (or no) variable, and combine the coefficients of the terms. For instance, if you have a+b where a and b are real numbers, you can combine them.
Unlike terms are terms in an equation that are different. These terms cannot be combined. Like terms, however, can be combined.
simplify means to get an expression to its simplest form (a.k.a. combine like terms, add together constants) i.e. x + x + 5 + 3 simplified is 2x + 8
mathematics: to combine terms that are alike
Combine like terms