X^2 + 9Y^2 + 4 - 6XY + 4X - 12Y
= (X^2 + 9Y^2 - 6XY) + (4X - 12Y) + 4
= (X - 3Y)^2 + 4(X - 3Y) + 4
= (X - 3Y + 2)^2
= (X - 1)^2 * (X - 2)^2