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Not sure what subject this is.

again the question is

$$\left(x-\frac12\right)^2$$

as a multiple choice question, i chose the answer:

$$x^2+\frac1x$$

Thank you.

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1  
Can you explain what's actually being asked? (x-(1/2))^x is an expression, not really a question. –  qaphla Jul 21 '13 at 4:27
    
What do you mean by "simplify"? Don't you mean "expand"? –  Pedro Tamaroff Jul 21 '13 at 4:36
1  
The obvious reason your answer is wrong is that $(x-1/2)^2$ is defined for $x=0$ but $x^2+1/x$ is undefined there... –  Thomas Andrews Jul 21 '13 at 6:08
    
Please do not change the question. You already posted the new, correct version of the question elsewhere, so there is no need to change this one. For one thing, changing the question you have is unfair to responders, especially when there is already an accepted answer and it has been a full day, and secondly there is no point in having two copies of the exact same question (when that happens, we close the copy as a duplicate). –  anon Jul 22 '13 at 5:10

1 Answer 1

up vote 3 down vote accepted

Assuming that in this case the (not terribly well-defined) term simplify actually means expand:

$$\left(x-\frac12\right)^2=\left(x-\frac12\right)\left(x-\frac12\right)=x^2-2\left(\frac12\right)x+\left(\frac12\right)^2=x^2-x+\frac14$$

This is just an application of the identity $(a+b)^2=a^2+2ab+b^2$.

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Ah, appreciate it Brian that makes sense. –  Joey Jul 21 '13 at 4:49
    
@Joey: You’re welcome. –  Brian M. Scott Jul 21 '13 at 4:51

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