Assuming you'd like to have it factored:
Given:
18x^4 + 12x^2y + 2y^2
First take out common factors to all three terms, 2
=2(9x^4+6x^2y+y^2)
Rewrite with x^2 as a group (attempting to factor as perfect square)
=2((3x^2)^2 + 2(3x^2)(y) + y^2)
factor into perfect square
=2(3x^2+y)^2
