Find the product. Simplify your answer. \[ (4 z-2)(2 z+2) \] \( \square \)

To find the product of \( (4z - 2)(2z + 2) \), we can use the distributive property (also known as the FOIL method). First, distribute \( 4z \) to both terms in the second factor: \[ 4z \cdot 2z = 8z^2 \] \[ 4z \cdot 2 = 8z \] Next, distribute \( -2 \) to both terms in the second factor: \[ -2 \cdot 2z = -4z \] \[ -2 \cdot 2 = -4 \] Now, we combine all these results: \[ 8z^2 + 8z - 4z - 4 \] Combine like terms: \[ 8z^2 + (8z - 4z) - 4 = 8z^2 + 4z - 4 \] Thus, the simplified answer is: \[ \boxed{8z^2 + 4z - 4} \]