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\frac{4a^{2}+12a+9}{4}
Factor out \frac{1}{4}.
\left(2a+3\right)^{2}
Consider 4a^{2}+12a+9. Use the perfect square formula, p^{2}+2pq+q^{2}=\left(p+q\right)^{2}, where p=2a and q=3.
\frac{\left(2a+3\right)^{2}}{4}
Rewrite the complete factored expression.