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When given an algrebraic expression of the form

$$ \ 6A + 7{A^2}\ $$

and asked to simplify, would the correct answer be

a) $$ \ A(6 + 7A)\ $$

or

b) That this cannot be simplified further

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You can factor out the $A$ from the first equation. I don't know however how "simple" would be defined in this context; either can be argued to be "simple". –  J. M. Sep 14 '10 at 12:35
    
I would suggest both a) and b) are both good answers depending on what you are using the expression for. For seeing roots of $6A+7A^2$ I would suggest $A(6+7A)$ is simplified. For typing into your calculator perhaps b) is simplified. –  alext87 Sep 14 '10 at 12:45

2 Answers 2

up vote 3 down vote accepted

"Simplify" is not particularly well-defined. For the expression by itself, I think (b) might be the more common textbook answer; if the expression were the denominator of a rational expression, (a) is more likely to be useful.

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There can be no meaningful answer without a prior definition of "simpler". What is simplest or most useful is highly context dependent. For example, in some particular contexts it might prove "simpler" to employ $\rm\;A^2 + 6A(A+1)\;$ instead of either of the above forms.

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