Chapter 4 - Quadratic Functions and Equations - 4-4 Factoring Quadratic Expressions - Practice and Problem-Solving Exercises - Page 222: 62

$3(2x+3)^2$

Factoring the $GCF= 3 ,$ the given expression, $ 12x^2+36x+27 ,$ is equivalent to \begin{align*} 3(4x^2+12x+9) \end{align*} Using $(x\pm y)^2=(x)^2\pm2(x\cdot y)+(y)^2$ or the square of a binomial, the factored form of the expression above is \begin{align*} & 3[(2x)^2+2(6x)+(3)^2] \\&= 3[(2x)^2+2(2x\cdot 3)+(3)^2] \\&= 3[(2x+3)^2] \\&= 3(2x+3)^2 \end{align*}