Simplifying
144uv4 + -388uv2 + 144u

Reorder the terms:
144u + -388uv2 + 144uv4

Factor out the Greatest Common Factor (GCF), '4u'.
4u(36 + -97v2 + 36v4)

Factor a trinomial.
4u((4 + -9v2)(9 + -4v2))

Factor a difference between two squares.
4u(((2 + 3v)(2 + -3v))(9 + -4v2))

Factor a difference between two squares.
4u(((3 + 2v)(3 + -2v))(2 + 3v)(2 + -3v))

Final result:
4u(2 + 3v)(2 + -3v)(3 + 2v)(3 + -2v)