To factor the expression 9x² + 30x + 25, we need to find two binomials that multiply together to give us this expression.

First, we look for two numbers that multiply to give 9x² (the coefficient of x²) and add up to 30x (the coefficient of x). The numbers that satisfy this condition are 3x and 3x, since (3x)(3x) = 9x² and 3x + 3x = 6x.

Next, we look for two numbers that multiply to give 25 (the constant term) and add up to 6x. The numbers that satisfy this condition are 5 and 5, since 5 * 5 = 25 and 5 + 5 = 10.

Therefore, we can factor the expression as (3x + 5)(3x + 5), or (3x + 5)².