Factor completely.

48w^2 + 120w +75=

3((5 + 4w)(5 + 4w))

is this correct??

yes it is

Though, to me, saying 3(4w+5)^2 is just as good. It is clear what the factors are. I wrote 4w+5 instead of 5+4w just because the polynomial was given in descending powers of w, so I made my factors read the same way.