Answer
$3x^2(y-3)^2$
Work Step by Step
For the polynomial
$$
3x^2y^2-18x^2y+27x^2= 3x^2(y^2-6y+9)
$$
we get a perfect square as follows
$$
3x^2y^2-18x^2y+27x^2= 3x^2(y^2-6y+9)=3x^2(y-3)^2
.$$
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