Which of the following is equivalent to -3x^4+30x^3-75x^2 7 -3x^2(x+5)(x-5) 3x^3(x+10)-25(3x^2) 3x^2(x+5)(x-5) -3x^2(x-5)(x-5)

To determine which of the given options is equivalent to $-3x^{4}+30x^{3}-75x^{2}$, we need to factor the expression.<br /><br />First, let's factor out the common factor of $-3x^2$ from each term:<br /><br />$-3x^{4}+30x^{3}-75x^{2} = -3x^2(x^2 - 10x + 25)$<br /><br />Now, we can factor the quadratic expression inside the parentheses:<br /><br />$x^2 - 10x + 25 = (x - 5)^2$<br /><br />So, the factored form of the original expression is:<br /><br />$-3x^2(x - 5)^2$<br /><br />Comparing this with the given options, we can see that the correct answer is:<br /><br />$-3x^{2}(x-5)(x-5)$<br /><br />Therefore, the equivalent expression is $-3x^{2}(x-5)(x-5)$.