1. - 12d - d +5t^3 + 12t^3 + 9d 2. 13x - 5z - 12x - 8x + 12z 3.7n^2 - 14n^2 + 15n^2 +12u + 13 u

Let's simplify each expression step by step. 1. **Expression:** \(-12d - d + 5t^3 + 12t^3 + 9d\) **Step 1:** Combine the \(d\) terms: \[ -12d - d + 9d = (-12 - 1 + 9)d = -4d \] **Step 2:** Combine the \(t^3\) terms: \[ 5t^3 + 12t^3 = (5 + 12)t^3 = 17t^3 \] **Final Result:** \[ -4d + 17t^3 \] 2. **Expression:** \(13x - 5z - 12x - 8x + 12z\) **Step 1:** Combine the \(x\) terms: \[ 13x - 12x - 8x = (13 - 12 - 8)x = -7x \] **Step 2:** Combine the \(z\) terms: \[ -5z + 12z = (12 - 5)z = 7z \] **Final Result:** \[ -7x + 7z \] 3. **Expression:** \(7n^2 - 14n^2 + 15n^2 + 12u + 13u\) **Step 1:** Combine the \(n^2\) terms: \[ 7n^2 - 14n^2 + 15n^2 = (7 - 14 + 15)n^2 = 8n^2 \] **Step 2:** Combine the \(u\) terms: \[ 12u + 13u = (12 + 13)u = 25u \] **Final Result:** \[ 8n^2 + 25u \] ### Summary of Results: 1. \(-4d + 17t^3\) 2. \(-7x + 7z\) 3. \(8n^2 + 25u\)