Why is this not the simplest form of this expression?
Matthew Harrington 
The precalculus text states the solution to a geometric series problem as: $2\sqrt{6}(\sqrt{2}+1)$
Why wouldn't we carry out the multiplication and say that the answer in simplest form is:
$2\sqrt{6}(\sqrt{2}+1)=2\sqrt{12}+2\sqrt{6} = 4\sqrt{3}+2\sqrt{6}$
3 Answers
$\begingroup$"Simplify" is a misleading term. What looks simpler to one person may be more complicated to someone else. Usually when an exercise in a book asks you to "simplify" it really means "do the operation we've been teaching you about in the chapter" such as factoring, expanding, etc. If it was a geometric series problem and they don't specifically tell you to simplify a certain way, either answer is fine.
$\endgroup$ $\begingroup$The way I see it, as long as your answer is correct and does not have any terms that can be simplified (e.g. an answer with $3\sqrt 6+2\sqrt 6$ wouldn't be correct), it doesn't matter if it is factored or not. Personally, I like to see the factored form, but others may like to see the expanded form. If I was marking your work, and the problem did not specify to factor or expand, I would accept both answers.
$\endgroup$ $\begingroup$For the particular case of a geometric series with initial term $a$ and ratio $r$, remember that the sum of the first $n$ terms is $a\frac{1-r^n}{1-r}$. Depending on the particularities of the series, it could be that the textbook, by showing the final answer as a product, may make the connection between the first term of the series and the ratio $\frac{1-r^n}{1-r}$.
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