ISt \( \left\lvert\, \begin{array}{l}\text { Multiply. } \\ 4 x\left(-8 x^{3}+3 x^{2}\right) \\ \begin{array}{l}\text { The product is } \\ \text { (Simplify your answer.) }\end{array}\end{array}\right. \)

When you multiply \(4x\) by \(-8x^{3}+3x^{2}\), you distribute \(4x\) to each term inside the parentheses. This gives you: \[ 4x \cdot (-8x^{3}) + 4x \cdot (3x^{2}) = -32x^{4} + 12x^{3}. \] So the simplified product is \(-32x^{4} + 12x^{3}\). Now you're left with a polynomial! It’s like a creative recipe, blending all those ingredients (terms) into a beautifully simplified dish. Each part contributes to the final flavor!