Tensor parallel-axis theorem ($I(P)=I(G)+M(|X{|}^{2}I-X{X}^T)$)

If $G$ is the center of mass and $X=P-G$, expanding the defining inertia tensor about $P$ gives the displayed formula. The cross terms vanish because $\int rdm=0$ in coordinates centred at $G$. Contracting with a unit axis $u$ gives the parallel axis theorem, with the squared distance between the parallel axes equal to $|X{|}^2-(u\cdot X{)}^2$.