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\frac{144x^{2}+1-24x}{9}
Factor out \frac{1}{9}.
\left(12x-1\right)^{2}
Consider 144x^{2}+1-24x. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=12x and b=1.
\frac{\left(12x-1\right)^{2}}{9}
Rewrite the complete factored expression.