We have the following:
[tex]16y^4-625x^4[/tex]factoring:
[tex]\begin{gathered} (4y^2)^2-(25x^2)^2=\mleft(4y^2+25x^2\mright)\mleft(4y^2-25x^2\mright)=(4y^2+25x^2)\mleft(2y+5x\mright)\mleft(2y-5x\mright) \\ \end{gathered}[/tex]Therefore, the answer is:
[tex]\mleft(4y^2+25x^2\mright)\mleft(2y+5x\mright)\mleft(2y-5x\mright)[/tex]