Match each problem with the correct answer: Prompts (1) Subtract and simplify completely: \( \left(-3 x^{2}-5 x+2\right)-(3 x-4) \) (2) Multiply and simplify completely: \( -6 x\left(-5 x^{2}+2 x+3\right) \)

Sure, let's solve each problem step by step and match them with their correct simplified answers. --- ### **Problem (1)** **Subtract and simplify:** \[ \left(-3 x^{2} - 5 x + 2\right) - (3 x - 4) \] **Solution:** 1. **Distribute the subtraction sign:** \[ -3x^2 - 5x + 2 - 3x + 4 \] 2. **Combine like terms:** \[ -3x^2 + (-5x - 3x) + (2 + 4) = -3x^2 - 8x + 6 \] **Answer:** \[ -3x^{2} - 8x + 6 \] --- ### **Problem (2)** **Multiply and simplify:** \[ -6x \left( -5x^{2} + 2x + 3 \right) \] **Solution:** 1. **Distribute \(-6x\) to each term inside the parentheses:** \[ (-6x)(-5x^2) + (-6x)(2x) + (-6x)(3) \] 2. **Perform the multiplication:** \[ 30x^3 - 12x^2 - 18x \] **Answer:** \[ 30x^{3} - 12x^{2} - 18x \] --- ### **Summary of Matches:** 1. **Problem (1):** \(-3x^{2} - 8x + 6\) 2. **Problem (2):** \(30x^{3} - 12x^{2} - 18x\)