  We show that Bogoliubov theory correctly predicts the low-energy spectral
properties of Bose gases in the Gross-Pitaevskii regime. We recover recent
results from \cite{BBCS,BBCS4}. While our main strategy is similar to the one
developed in \cite{BBCS,BBCS4}, we combine it with new ideas, taken in part
from \cite{Hainzl,NT}; this makes our proof substantially simpler and shorter.
As an important step towards the proof of Bogoliubov theory, we show that
low-energy states exhibit complete Bose-Einstein condensation with optimal
control on the number of orthogonal excitations.
