# How do you factor #12x^2 + 36xy + 27y^2?

##### 2 Answers
Jun 8, 2015

$f \left(x\right) = 3 \left(4 {x}^{2} + 12 x y + 9 {y}^{2}\right) = 3 {\left(2 x + 3 y\right)}^{2}$

Jun 8, 2015

Answer: $12 {x}^{2} + 36 x y + 27 {y}^{2} = 3 {\left(2 x + 3 y\right)}^{2}$

Problem: Factor $12 {x}^{2} + 36 x y + 27 {y}^{2}$.

Factor out the GCF $3$.

$3 \left(4 {x}^{2} + 12 x y + 9 {y}^{2}\right)$

$\left(4 {x}^{2} + 12 x y + 9 {y}^{2}\right)$ is a perfect square trinomial with the pattern

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$.

$a = 2 x$
$b = 3 y$

$\left(4 {x}^{2} + 12 x y + 9 {y}^{2}\right) = {\left(2 x + 3 y\right)}^{2}$

$12 {x}^{2} + 36 x y + 27 {y}^{2} = 3 {\left(2 x + 3 y\right)}^{2}$