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"Like terms" are terms whose variables (and their exponents such as the 2 in x2) are the same. In other words, terms that are "like" each other.
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In the future please be more specific as to what you are asking. Factoring: 2 x 2 x 2 x 29 In other terms: 23 x 29 or 8 x 29
A Taylor expansion is a way of representing a function in terms of a sum of its derivatives. Please see the link.
When you have an expression consisting of several terms added together, and they are not all like terms, and there are like terms separated by unlike terms, you use the commutative law of addition to rearrange the terms so that the like terms are next to each other.