(2) \( -4 m\left(2 m^{2}+5 m^{3}-3\right) \)

Let's expand the expression \( -4m\left(2m^{2} + 5m^{3} - 3\right) \). **Step-by-Step Expansion:** 1. **Distribute \(-4m\) across each term inside the parentheses:** \[ -4m \cdot 2m^{2} + (-4m) \cdot 5m^{3} + (-4m) \cdot (-3) \] 2. **Multiply each term:** \[ -8m^{3} - 20m^{4} + 12m \] 3. **Rearrange the terms in standard polynomial form (highest degree first):** \[ -20m^{4} - 8m^{3} + 12m \] **Final Expanded Form:** \[ -20m^{4} - 8m^{3} + 12m \] **Factorization (Optional):** If you'd like to factor the expression further, you can factor out the greatest common factor (GCF), which is \(-4m\): \[ -20m^{4} - 8m^{3} + 12m = -4m(5m^{3} + 2m^{2} - 3) \] Since the cubic polynomial \(5m^{3} + 2m^{2} - 3\) doesn't factor neatly with rational coefficients, the fully factored form is: \[ -4m(5m^{3} + 2m^{2} - 3) \] **Summary:** - **Expanded Form:** \(-20m^{4} - 8m^{3} + 12m\) - **Factored Form:** \(-4m(5m^{3} + 2m^{2} - 3)\)