Why do you think we dont hear from the "peaceful" muslims when this violence is going on?
Because tacitly they sympathise with the extremists.
At the end of the day they value solidarity among Muslims over any other allegiances they may have.
Ask your Muslim friends to explain the following verses from the Quran:
Quran (8:55) - Surely the vilest of animals in Allah's sight are those who disbelieve
Quran (48:29) - Muhammad is the messenger of Allah. And those with him are hard (ruthless) against the disbelievers and merciful among themselves
Quran (9:30) - And the Jews say: Ezra is the son of Allah, and the Christians say: The Messiah is the son of Allah... Allah (Himself) fights against them. How perverse are they!
Quran (8:12) - I will cast terror into the hearts of those who disbelieve. Therefore strike off their heads and strike off every fingertip of them
Qur'an (9:123) - O you who believe! Fight those of the unbelievers who are near to you and let them find in you hardness
Quran (5:33) - The punishment of those who wage war against Allah and His messenger and strive to make mischief in the land is only this, that they should be murdered or crucified or their hands and their feet should be cut off on opposite sides or they should be imprisoned; this shall be as a disgrace for them in this world, and in the hereafter they shall have a grievous chastisement
This is just a few. And before the resident extreme leftists weigh in and start making comparison to the old testament in the Christian bible.
Christianity went through the reformation and the new testament is mans new contract with god.
The old Testament is still relevant but any contradictions are overridden by the new testament. This is known as abrogation - essentially where there is conflicting messages, the newer passages override the old.
The Quran is also governed by abrogation which reveals an interesting dichotomy between Islam and Christianity.
Whilst Christianity had all its bloodthirstiness in the old testament, the Quran is the other way around.
All the peaceful verses that muslims are so fond of quoting are Muhammad's early work, before he became a powerful warlord.
What Muslims don't want to admit is that the peaceful verses of the quran are made redundant by the later warlike verses.
For example:
4:15-16 says this:
"Against those of your women who commit adultery, call witnesses four in number from among yourselves; and if these bear witness, then keep the women in houses until death release them, or God shall make for them a way.
And if two of you commit it, then hurt them both; but if they turn again and amend, leave them alone, verily, God is easily turned, compassionate."
While 24:2 has an entirely different prescription:
"The adulteress and the adulterer you shall whip each of them a hundred lashes. Do not be swayed by pity from carrying out GOD's law, if you truly believe in GOD and the Last Day. And let a group of believers witness their penalty."
Also there are the verses that deal with the proper treatment of Christians and Jews:
"Thou wilt surely find that the strongest in enmity against those who believe are the Jews and the idolaters; and thou wilt find the nearest in love to those who believe to be those who say, 'We are Christians;' that is because there are amongst them priests and monks, and because they are not proud." (5:82)
Yet in 5:51 we read the following command:
"O you who believe! do not take the Jews and the Christians for friends; they are friends of each other; and whoever amongst you takes them for a friend, then surely he is one of them; surely Allah does not guide the unjust people."
So in summary, moderate muslims don't speak up because they know that there is in truth there is a stronger theological argument for the extremists position than their own moderate interpretations.
Don't believe me, read about abrogation in Islam and see for yourself.