b) \( 12 p^{3}-75 p x^{2} \)

To factor out the expression \( 12p^3 - 75px^2 \), first, we identify the greatest common factor (GCF) of the coefficients and the variables. The GCF here is \( 3p \). So, we can factor it out: \( 12p^3 - 75px^2 = 3p(4p^2 - 25x^2) \). Now, notice that \( 4p^2 - 25x^2 \) is a difference of squares, which can be further factored: \( 4p^2 - 25x^2 = (2p - 5x)(2p + 5x) \). Putting it all together, the fully factored form of the expression is: \( 12p^3 - 75px^2 = 3p(2p - 5x)(2p + 5x) \).