1. **State the problem:** Simplify or analyze the expression $d^2 + 8d^3r^5 + 15rx^2$. 2. **Identify terms:** The expression consists of three terms: $d^2$, $8d^3r^5$, and $15rx^2$. 3. **Check for like terms:** Like terms have the same variables raised to the same powers. Here, each term has different variables and powers, so they cannot be combined. 4. **Final expression:** Since no terms can be combined, the simplified form remains: $$d^2 + 8d^3r^5 + 15rx^2$$ This is the simplest form of the given expression.