# How do you factor 4x^2+9+12x using the perfect squares formula?

${\left(2 x + 3\right)}^{2}$
The perfect squares formula says that ${a}^{2} + 2 a b + {b}^{2} = {\left(a + b\right)}^{2}$
You can see $4 {x}^{2} + 9 + 12 x$ as ${2}^{2} {x}^{2} + {3}^{2} + \left(3 \cdot 2\right) x = {\left(2 x\right)}^{2} + \left(3 \cdot 2\right) x + {3}^{2}$
In this case you have $a = 2 x$, $b = 3$ and $2 a b = 2 \left(2 x \cdot 3\right) = \left(2 \cdot 2 \cdot 3\right) x = 12 x$