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