Find the product. Simplify your answer. \( u\left(-4 u^{2}+6\right) \)

To find the product \( u\left(-4 u^{2}+6\right) \), you distribute \( u \) across the terms in the parentheses. This gives: \[ u \cdot (-4 u^{2}) + u \cdot 6 = -4u^{3} + 6u \] So the simplified answer is: \[ -4u^{3} + 6u \] Now, let's explore some additional insights! First, did you know that polynomials like this one can represent real-world scenarios? For example, in physics, equations modeling projectile motion can be quadratic or cubic, similar to your expression. Analyzing these can help us predict the trajectory of an object! Furthermore, always keep an eye out for the common mistake of forgetting the negative sign when distributing! Double-checking your work after each step can save you from that pesky error.