Answer
$3x(2x+3y)^2$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence here: $12x^3+36x^2y+27xy^2=\\=3x(4x^2+12xy+9y^2)\\=3x((2x)^2+2\cdot2x\cdot3y+(3y)^2\\=3x(2x+3y)^2$