7. Let $x_{1}, x_{2}, x_{3}$ be greater than 0, and $x_{1}+x_{2}+x_{3}=1$, then the maximum value of $x_{1} x_{2}^{2} x_{3}+x_{1} x_{2} x_{3}^{2}$ is
\begin{array}{l}\text { 7. Original expression }=x_{1} x_{2} x_{3}\left(x_{2}+x_{3}\right)=\frac{1}{12}\left(3 x_{1}\right)\left(2 x_{2}\right)\left(2 x_{3}\right)\left(x_{2}+x_{3}\right) \\ =\frac{1}{12} \cdot\left[\frac{3\left(x_{1}+x_{2}+x_{3}\right)}{4}\right]^{\prime}=\frac{27}{1024} \text {, } \\ \text { when } x_{1}=\frac{1}{4}, x_{2}=x_{3}=\frac{3}{8} \text {, the maximum value is } \frac{27}{1024} \text {. } \\\end{array}