1. **State the problem:** Simplify or analyze the expression $2\sin^3(x)(x^2-1)$. 2. **Understand the components:** The expression is a product of $2$, $\sin^3(x)$ (which means $\sin(x)$ cubed), and $(x^2 - 1)$. 3. **Recall important identities:** The term $(x^2 - 1)$ can be factored as $(x-1)(x+1)$. The sine function is periodic and bounded between -1 and 1. 4. **Rewrite the expression:** $$2\sin^3(x)(x^2-1) = 2\sin^3(x)(x-1)(x+1)$$ 5. **Interpretation:** This expression is a product of a trigonometric function cubed and a quadratic factorized polynomial. It can be used as is or further analyzed depending on the context (e.g., finding zeros, graphing). 6. **Zeros of the expression:** The expression equals zero when any factor is zero: - $\sin(x) = 0$ - $x-1=0 \Rightarrow x=1$ - $x+1=0 \Rightarrow x=-1$ 7. **Summary:** The expression is $2\sin^3(x)(x-1)(x+1)$ and zeros occur at $x = n\pi$ for integers $n$, and at $x=\pm 1$.