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\frac{a^{2}-6a+9}{4}
Factor out \frac{1}{4}.
\left(a-3\right)^{2}
Consider a^{2}-6a+9. Use the perfect square formula, p^{2}-2pq+q^{2}=\left(p-q\right)^{2}, where p=a and q=3.
\frac{\left(a-3\right)^{2}}{4}
Rewrite the complete factored expression.