Find the product . Simplify your answer. -2x(3x^2+x+4) square

To find the product and simplify the expression \(-2x(3x^2 + x + 4)\), we need to distribute \(-2x\) to each term inside the parentheses.<br /><br />First, distribute \(-2x\) to \(3x^2\):<br />\[<br />-2x \cdot 3x^2 = -6x^3<br />\]<br /><br />Next, distribute \(-2x\) to \(x\):<br />\[<br />-2x \cdot x = -2x^2<br />\]<br /><br />Finally, distribute \(-2x\) to \(4\):<br />\[<br />-2x \cdot 4 = -8x<br />\]<br /><br />Now, combine all these results:<br />\[<br />-6x^3 - 2x^2 - 8x<br />\]<br /><br />Thus, the simplified product is:<br />\[<br />\boxed{-6x^3 - 2x^2 - 8x}<br />\]