Question

is 2(2n-3)(2n+3) a difference of squares?
is 3(2x+3)^2 a perfect square trinomial?

Answer 1

$2(2n+3)(2n-3)$ is not a difference of squares. It expands to $8n^2-18$, whose two terms are not perfect squares.

For $3(2x+3)^2$, I think the same thing applies, that having a 3 factored-out means it isn't a perfect-square trinomial. A perfect-square trinomial is, very simply, the result of squaring two binomials. I would say that it's kind of sketchy here, but it's obviously not a trinomial in this form, because there are only two terms, so I would say no.