2. Expression: \( 4(2 a+5)-3(3 a-7)+12 \)

To simplify the expression \( 4(2a + 5) - 3(3a - 7) + 12 \), follow these steps: 1. **Distribute the Multiplication:** Apply the distributive property \( a(b + c) = ab + ac \) to each term inside the parentheses. \[ 4(2a) + 4(5) - 3(3a) + 3(7) + 12 \] Simplify each term: \[ 8a + 20 - 9a + 21 + 12 \] 2. **Combine Like Terms:** - **Combine the terms with \( a \):** \[ 8a - 9a = -a \] - **Combine the constant terms:** \[ 20 + 21 + 12 = 53 \] So, the expression becomes: \[ -a + 53 \] 3. **Final Simplified Expression:** It's common to write the constant term first, so you can also write: \[ 53 - a \] **Answer:** The simplified expression is \( 53 - a \).