A) \[{{\left( a+\frac{1}{2} \right)}^{2}}\]
B) \[\left( a+\frac{1}{2} \right)(a+2)\]
C) \[\left( a+\frac{1}{2} \right)\left( a-\frac{1}{2} \right)\]
D) \[{{\left( a-\frac{1}{2} \right)}^{2}}\]
Correct Answer: A
Solution :
\[\left( {{a}^{2}}+a+\frac{1}{4} \right)={{a}^{2}}+\frac{1}{2}a+\frac{1}{2}a+\frac{1}{4}\] \[=a\left( a+\frac{1}{2} \right)+\frac{1}{2}\left( a+\frac{1}{2} \right)\] \[=\left( a+\frac{1}{2} \right)\left( a+\frac{1}{2} \right)={{\left( a+\frac{1}{2} \right)}^{2}}\]
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