How do you factor a "perfect square trinomial" 16x^2+48x+36 ?

Apr 10, 2015

First, you can divide by a common factor, which is 4 here.

$= 4 {x}^{2} + 12 x + 9$

Then factor like normal, but it's just a little harder since it's not ${x}^{2}$ but $4 {x}^{2}$. You have either $2 x \cdot 2 x$ or $4 x \cdot x$. But you said it's a "perfect square trinomial", so it must be $2 x \cdot 2 x$.

$= \left(2 x + 3\right) \left(2 x + 3\right)$

$= 4 \left(2 x + 3\right) \left(2 x + 3\right) = 4 {\left(2 x + 3\right)}^{2}$