The best way to factorize the given quadratic expression 25x^2 - 30x + 5, is to first look for the greatest common factor.
The greatest common factor that can be extracted out of the coefficients 25, -30 and 5 is 5. After factoring out 5, the expression now looks like this:
5*(5x^2 - 6x + 1)
Now, we have a quadratic in the form of ax^2 + bx + c where a =5, b=-6 and c=1. We aim to factorize the quadratic in the form of (px-q)(rx-s).
To do this, we need to find two numbers that add up to be -6, and multiply to be 5, that is, they should satisfy the equation, pr = 5 and q + s = -6.
The numbers that fulfill these requirements are -5 and -1. Therefore, the quadratic can be factorized as (5x-1)(x-1).
Finally, multiplying in 5 that was factored out at the beginning, we have:
y = 5(5x - 1)(x - 1)
So, the correct factorization is option b, y = 5(5x - 1)(x - 1).