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Rearranging terms is an essential step when working through algebraic expressions. It means organizing the expression in such a way that like terms are grouped together. Like terms are terms that have the same variables or constant multiplier. For example:

• The terms \(9n\) and \(15n\) are like terms because they both involve the variable \(n\).
• The constants \(10\) and \(7\) are also like terms as they are standalone numbers without variables.

To rearrange terms effectively, simply move them around in the expression so that like terms are next to each other. This step is crucial because it sets you up for easier computation in the following steps. Rearranging does not change the value of the expression, it's like tidying up before you begin to calculate. With our example, after rearranging we have: \(9n + 15n + 10 + 7\).
By placing all similar terms together, future steps like combining and simplifying become much more straightforward.

The distributive property is a fundamental principle in algebra, but it's often not directly seen when combining like terms. Nevertheless, it's beneficial to understand how it applies so you can use it in more complex problems. The distributive property states that a single term multiplied by terms inside a parenthesis can be "distributed" across each term inside. For instance, for terms like \(a(b + c)\), you can rewrite it as \(ab + ac\). In our exercise, after rearranging the terms, the distributive property helps when you want to "factor out" a particular variable. So for example, if you had something like \(9n + 15n\), it can be seen as \((9 + 15)n\). However, since combining like terms in this case uses simple addition between like terms \(9n\) and \(15n\) to make \(24n\), the property shows that both processes are consistent in principles used.Understand that the distributive property is always working in the background even if not explicitly shown in every problem.

Simplifying expressions is the ultimate goal when working on algebraic problems. It means reducing an expression to its simplest form where no like terms remain uncombined. Starting with the previously rearranged terms, combining is the next step.

• First, add the like terms that have the variable \(n\): \(9n + 15n = 24n\).
• Then, add the constant like terms: \(10 + 7 = 17\).

The expression is simplified when all like terms are combined. For our expression, after combining we get \(24n + 17\), which is the simplest form as no further combinations are needed.
Simplification doesn’t change the value of the expression in terms of its outcome when calculated; it just makes it shorter and easier to read or use in further calculations. The simplification step ensures that you have the most optimal expression to work with next, especially when additional math operations are involved.