Question:
Factorize: \[ 21x^2-2x+\frac{1}{21} \]
Solution:
\[ 21x^2-2x+\frac{1}{21} \]
\[ =21x^2-2\left(x\cdot\frac{1}{21}\right)+\frac{1}{21^2}\cdot21 \]
\[ =21\left(x^2-\frac{2x}{21}+\frac{1}{441}\right) \]
\[ =21\left(x-\frac{1}{21}\right)^2 \]
\[ =\left(\sqrt{21}x-\frac{1}{\sqrt{21}}\right)^2 \]
\[ \boxed{21\left(x-\frac{1}{21}\right)^2} \]