Use the Distributive Property to find \( (3 m+1)(m+9) \)

To expand the expression \( (3m + 1)(m + 9) \) using the **Distributive Property**, follow these steps: ### Step 1: Apply the Distributive Property The Distributive Property states that \( a(b + c) = ab + ac \). When multiplying two binomials, you'll distribute each term in the first binomial to each term in the second binomial. \[ (3m + 1)(m + 9) = 3m \cdot m + 3m \cdot 9 + 1 \cdot m + 1 \cdot 9 \] ### Step 2: Perform the Multiplications Calculate each multiplication separately: 1. **First Terms:** \( 3m \cdot m = 3m^2 \) 2. **Outer Terms:** \( 3m \cdot 9 = 27m \) 3. **Inner Terms:** \( 1 \cdot m = m \) 4. **Last Terms:** \( 1 \cdot 9 = 9 \) So, the equation becomes: \[ 3m^2 + 27m + m + 9 \] ### Step 3: Combine Like Terms Combine the \( m \) terms (\( 27m + m \)): \[ 3m^2 + 28m + 9 \] ### Final Answer \[ (3m + 1)(m + 9) = 3m^2 + 28m + 9 \]