Find the product. Simplify your answer. \( (4 q-4)\left(2 q^{2}+q-1\right) \)

To find the product of \((4q - 4)(2q^2 + q - 1)\), we can use the distributive property (also known as the FOIL method for two binomials). First, let's factor out the common term in the first expression: \[ 4(q - 1)(2q^2 + q - 1) \] Now, we distribute \(4(q - 1)\) into \((2q^2 + q - 1)\): 1. Multiply \(4(q)\) by each term of \((2q^2 + q - 1)\): \[ 4q \cdot 2q^2 = 8q^3 \] \[ 4q \cdot q = 4q^2 \] \[ 4q \cdot (-1) = -4q \] 2. Multiply \(-4\) by each term of \((2q^2 + q - 1)\): \[ -4 \cdot 2q^2 = -8q^2 \] \[ -4 \cdot q = -4q \] \[ -4 \cdot (-1) = 4 \] Now combining all these results: \[ 8q^3 + 4q^2 - 4q - 8q^2 - 4q + 4 \] Next, we combine like terms: \[ 8q^3 + (4q^2 - 8q^2) + (-4q - 4q) + 4 \] \[ = 8q^3 - 4q^2 - 8q + 4 \] Thus, the final simplified answer is: \[ \boxed{8q^3 - 4q^2 - 8q + 4} \]