Question 41574
First, you'll notice that the first and last terms of your expression are perfect squares:
{{{9x^2 = (3x)^2}}} and {{{25y^2 = (5y)^2}}}

Using this fact as a clue, and since you know that: {{{(A+B)^2 = A^2 + 2AB + B^2}}} you might try:

{{{(3x + 5y)^2}}} as factors.
 Check using FOIL.

{{{(3x+5y)(3x+5y) = 9x^2 + 15xy + 15xy + 25y^2}}} Simplify:
{{{9x^2 + 30xy + 25y^2}}}

So the factors of: {{{9x^2 + 30xy + 25y^2 = (3x + 5y)(3x + 5y)}}}