Find the product. Simplify your answer. \( (2 g+4)\left(2 g^{2}+2 g-2\right) \)

To find the product \( (2g + 4)(2g^2 + 2g - 2) \), use the distributive property (also known as the FOIL method for binomials): 1. Multiply \( 2g \) by each term in the second polynomial: - \( 2g \cdot 2g^2 = 4g^3 \) - \( 2g \cdot 2g = 4g^2 \) - \( 2g \cdot (-2) = -4g \) 2. Next, multiply \( 4 \) by each term in the second polynomial: - \( 4 \cdot 2g^2 = 8g^2 \) - \( 4 \cdot 2g = 8g \) - \( 4 \cdot (-2) = -8 \) Now combine all these results: \[ 4g^3 + 4g^2 - 4g + 8g^2 + 8g - 8 \] Combine like terms: \[ 4g^3 + (4g^2 + 8g^2) + (-4g + 8g) - 8 \] This simplifies to: \[ 4g^3 + 12g^2 + 4g - 8 \] So, the product simplified is: \[ \boxed{4g^3 + 12g^2 + 4g - 8} \]