1. **State the problem:** Show the expression $\cos^3(x) \sin^2(x)$ and understand its form. 2. **Recall the definitions:** $\cos^3(x)$ means $(\cos(x))^3$ and $\sin^2(x)$ means $(\sin(x))^2$. 3. **Rewrite the expression:** $$\cos^3(x) \sin^2(x) = (\cos(x))^3 \times (\sin(x))^2$$ 4. **No further simplification is possible without additional context or identities.** 5. **If needed, use trigonometric identities:** For example, $\sin^2(x) = 1 - \cos^2(x)$, so $$\cos^3(x) \sin^2(x) = \cos^3(x) (1 - \cos^2(x)) = \cos^3(x) - \cos^5(x)$$ This shows the expression in terms of powers of cosine only. **Final answer:** $$\cos^3(x) \sin^2(x) = \cos^3(x) - \cos^5(x)$$