# How do you know if 9x^2 +12x - 4 is a perfect square trinomial and how do you factor it?

Jun 7, 2015

$\textcolor{b l u e}{9 {x}^{2}}$ is a perfect square : $= \textcolor{b l u e}{{\left(3 x\right)}^{2}}$
$\textcolor{red}{4}$ is also a perfect square : $= \textcolor{red}{{2}^{2}}$
And $\textcolor{p u r p \le}{12 x} = 2 \cdot \textcolor{b l u e}{3 x} \cdot \textcolor{red}{2}$

We know that (color(blue)a-color(red)b)²=color(blue)(a^2)-2color(blue)acolor(red)b+color(red)(b^2)
And (color(blue)a+color(red)b)²=color(blue)(a^2)+2color(blue)acolor(red)b+color(red)(b^2)

But here we have $\textcolor{b l u e}{{a}^{2}} + 2 \textcolor{b l u e}{a} \textcolor{red}{b} - \textcolor{red}{{b}^{2}}$

This isn't a perfect square trinomial, so we can't factor it.