Let a, b and c be three unit vectors such that | a - b |^2+| a - c |^2=8. Then | a +2 b |^2+| a +2 c |^2 is equal to \ \ \ \.

Let $\displaystyle \vec{a}, \vec{b}$ and $\displaystyle \vec{c}$ be three unit vectors such that $\displaystyle |\vec{a}-\vec{b}|^2+|\vec{a}-\vec{c}|^2=8$. Then $\displaystyle |\overrightarrow{\mathrm{a}}+2 \overrightarrow{\mathrm{~b}}|^2+|\overrightarrow{\mathrm{a}}+2 \overrightarrow{\mathrm{c}}|^2$ is equal to \_\_\_\_.