1. **State the problem:** Expand and simplify the expression $ (z + 4)(z - 2) $. 2. **Use the distributive property (FOIL method):** Multiply each term in the first parenthesis by each term in the second parenthesis. $$ (z + 4)(z - 2) = z \cdot z + z \cdot (-2) + 4 \cdot z + 4 \cdot (-2) $$ 3. **Calculate each product:** $$ z \cdot z = z^2 $$ $$ z \cdot (-2) = -2z $$ $$ 4 \cdot z = 4z $$ $$ 4 \cdot (-2) = -8 $$ 4. **Combine all terms:** $$ z^2 - 2z + 4z - 8 $$ 5. **Simplify by combining like terms:** $$ -2z + 4z = 2z $$ 6. **Final simplified expression:** $$ z^2 + 2z - 8 $$ This is the expanded and simplified form of the given expression.