You are wrong. The Quran explicitly forbids killing. There are references to what you say in the reported sayings of Mohammed, but these are not the Quran, and it is not expected that they all really come from Mohammed. There are references to fighting the Unbelievers in the Quran (cf. Surah 48:29 and Surah 47:4), but they explicity refer to holding prisoners.

You might also want to keep in mind that Islam is directly descended from the same religions that became Judaism and Christianity. They all believe in the same God. The reason that Islam believes that Jews and Christians are unbelievers is because they believe in other Gods, Ezra (Surah 9:30) and Jesus (ibid. and Surah 5:72).

So you might want to consider what it is that you ``know''.