Which of the following is equivalent to the difference: \( \left(-3 x^{2}+5 x-1\right)-\left(4 x^{2}-3 x+7\right) \) (1) \( 7 x^{2}-8 x+8 \) (2) \( -7 x^{2}+8 x-8 \) (3) \( x^{2}+2 x-8 \) (4) \( -x^{2}-2 x+8 \)

To find the equivalent expression for the difference \( \left(-3 x^{2}+5 x-1\right)-\left(4 x^{2}-3 x+7\right) \), we first need to distribute the negative sign across the second polynomial: \[ -3x^{2} + 5x - 1 - 4x^{2} + 3x - 7 \] Now, combine like terms: 1. For the \( x^{2} \) terms: \(-3x^{2} - 4x^{2} = -7x^{2}\) 2. For the \( x \) terms: \(5x + 3x = 8x\) 3. For the constant terms: \(-1 - 7 = -8\) Putting it all together, we have: \[ -7x^{2} + 8x - 8 \] So, the equivalent expression is: (2) \( -7 x^{2}+8 x-8 \)