Combine the following expressions. \( r \sqrt{t}+s \sqrt{t} \) \( \sqrt{r s+2 t} \) \( (r+s) \sqrt{t} \) \( (r-s) \sqrt{t} \)

Simplify the expression by following steps: - step0: Solution: \(r\sqrt{t}+s\sqrt{t}\) Calculate or simplify the expression \( \sqrt(r * s + 2 * t) \). Simplify the expression by following steps: - step0: Solution: \(\sqrt{rs+2t}\) Calculate or simplify the expression \( (r - s) * \sqrt(t) \). Simplify the expression by following steps: - step0: Solution: \(\left(r-s\right)\sqrt{t}\) - step1: Distribute \(\sqrt{t}:\) \(r\sqrt{t}-s\sqrt{t}\) Calculate or simplify the expression \( (r + s) * \sqrt(t) \). Simplify the expression by following steps: - step0: Solution: \(\left(r+s\right)\sqrt{t}\) - step1: Distribute \(\sqrt{t}:\) \(r\sqrt{t}+s\sqrt{t}\) Let's combine the given expressions step by step: 1. **First Expression:** \[ r \sqrt{t} + s \sqrt{t} \] This can be simplified to: \[ (r + s) \sqrt{t} \] 2. **Second Expression:** \[ \sqrt{r s + 2 t} \] This expression remains as is since it cannot be simplified further. 3. **Third Expression:** \[ (r + s) \sqrt{t} \] This is already in its simplest form. 4. **Fourth Expression:** \[ (r - s) \sqrt{t} \] This is also in its simplest form. ### Summary of Combined Expressions: - The first and third expressions are equivalent: \[ (r + s) \sqrt{t} \] - The second expression is: \[ \sqrt{r s + 2 t} \] - The fourth expression is: \[ (r - s) \sqrt{t} \] Thus, the combined expressions are: 1. \( (r + s) \sqrt{t} \) 2. \( \sqrt{r s + 2 t} \) 3. \( (r - s) \sqrt{t} \)