Enter the coefficients for each term in the product of \( 9 w^{2} \) and \( 4 w-1 \). Enter 0 as the coefficient of any terms not in the product. \( (\square) w^{3}+(\square) w+(\square) \)

Let's multiply the two expressions step by step. 1. **Write the product:** We are multiplying \[ 9w^2 \quad \text{and} \quad 4w - 1. \] 2. **Distribute \(9w^2\) through the second expression:** Multiply \(9w^2\) by each term in \(4w - 1\): - \(9w^2 \times 4w = 36w^3\) - \(9w^2 \times (-1) = -9w^2\) Thus, the product is: \[ 36w^3 - 9w^2. \] 3. **Identify the missing terms in the given expression:** The problem asks for the coefficients for each term in the product expressed as: \[ (\square)w^3 + (\square)w + (\square). \] Notice that the product we obtained is \(36w^3 - 9w^2\). Here, we have a term with \(w^3\) and a term with \(w^2\) (which is not requested), and there are no terms with \(w\) or a constant. 4. **Fill in the coefficients:** - The coefficient of \(w^3\) is \(36\). - There is no \(w\) term, so its coefficient is \(0\). - There is no constant term, so its coefficient is \(0\). Thus, the completed expression is: \[ 36w^3 + 0w + 0. \] **Final Answer:** \(36\) for the \(w^3\) term, \(0\) for the \(w\) term, and \(0\) for the constant term.