1. **Stating the problem:** Simplify or understand the expression $(x+a) \sqrt{2x+1}$. 2. **Formula and rules:** The expression involves a binomial $(x+a)$ multiplied by a square root $\sqrt{2x+1}$. We cannot simplify the square root unless $2x+1$ is a perfect square or can be factored further. 3. **Intermediate work:** Since there is no further factorization or simplification possible without additional information about $a$ or $x$, the expression remains as is: $$ (x+a) \sqrt{2x+1} $$ 4. **Explanation:** This expression represents the product of the binomial $(x+a)$ and the square root of the linear expression $2x+1$. Without specific values or conditions, this is the simplest form. **Final answer:** $$ (x+a) \sqrt{2x+1} $$