Getting the AdS metric from maximally symmetric spaces

Question

I am familiar with the way we derive the form of the FRW metric by just using the fact that we have a maximally symmetric space i.e the universe is homogeneous and isotropic in spatial coordinates. Similarly, how do I get the Poincare patch of $AdS_{p+2}$ i.e \begin{equation} ds^2 = R^{2}\left(\frac{du^2}{u^2}+u^2(-dt^2+d\mathbf{x}^2)\right) \end{equation} by using the property of maximal symmetry only.