0. \( \quad 2(8 p-3 q)\left(p-3+q^{2}\right) \)

To expand the expression: \[ 2(8p - 3q)\left(p - 3 + q^{2}\right) \] follow these steps: ### Step 1: Expand the Inner Product First, expand the product \((8p - 3q)(p - 3 + q^{2})\): \[ (8p - 3q)(p - 3 + q^{2}) = 8p \cdot p + 8p \cdot (-3) + 8p \cdot q^{2} - 3q \cdot p - 3q \cdot (-3) - 3q \cdot q^{2} \] Calculate each term: \[ \begin{align*} 8p \cdot p &= 8p^{2} \\ 8p \cdot (-3) &= -24p \\ 8p \cdot q^{2} &= 8p q^{2} \\ -3q \cdot p &= -3p q \\ -3q \cdot (-3) &= 9q \\ -3q \cdot q^{2} &= -3q^{3} \\ \end{align*} \] Combine all the terms: \[ 8p^{2} - 24p + 8p q^{2} - 3p q + 9q - 3q^{3} \] ### Step 2: Multiply by 2 Now, multiply the entire expression by 2: \[ 2 \times (8p^{2} - 24p + 8p q^{2} - 3p q + 9q - 3q^{3}) = 16p^{2} - 48p + 16p q^{2} - 6p q + 18q - 6q^{3} \] ### Final Expanded Form The fully expanded form of the original expression is: \[ 16p^{2} - 48p + 16p q^{2} - 6p q + 18q - 6q^{3} \]