If you're scared of violent Islamic jihad (and everyone should be) then you should at least entertain the idea that fighting it with conventional warfare, whether in Gaza or Afghanistan or Iraq or with drones or standing armies, will only feed it. It is an ideology that does not limit itself to political borders and it's primary tactic is fear-based propaganda and therefore it does not generally define victory in terms of conquered land or body count, rather it strives for influence.
The past 20 years have seen a fundamental change in the way information travels which has given rise to a fundamental difference in the way humans relate to each other: we are now spectacularly interconnected, and now ideas can spread throughout populations without central control. It's more democratic and unpredictable, and there are fewer and fewer choke points where you can control it.
Traditional warfare is designed to control the choke point of a government and it's influence on its population. When you are dealing with an adversary who's primary mode of operation is via traditional government power, then this is an effective tactic. This is why World War II was so tidy - the offending aspects of Nazi Germany and Japan were so highly concentrated in government structure that you could bomb that government structure into submission and solve your problem. Islomofascism on the other hand has concentrated all of its power in the abstract ideas such as religious interpretation, narratives about cultural identity and a claim to being a counterpoint to Western aggression, and there is no similar choke point for traditional warfare to attack.
The modern face of terrorism is ultimately nothing more than a tactic they use to spread these abstract ideas, and it has been uniquely effective at using the new environment of global information flow to do this. Its success is completely independent of whether a particular entity named Hamas or Al Qaida or Sadam Hussein is in power, and instead it is wholly dependent on how individuals react to their environment and how their personal experiences affect the narrative that is spreading throughout the global information environment.
This is why Governments who are fighting against terrorism need to shift away from relying on conventional warfare and instead meet the terrorists in this new battleground of ideas and narratives. Islamic Jihad has grown in leaps and bounds over the past 15 years because they have played the long game and have been able to slowly grow the idea that the West is imperial, violent, selfish, greedy, and that it will corrupt local cultures. Whether or not this is true, this is the narrative that is out there, and every time Israel invades Gaza or the US launches a drone strike it becomes a little more common or a little more engrained in Muslim or Arab culture and identity. The terrorists are only fanning this flame by launching various small scale attacks that invite a heavy military response from Western governments.
Governments need to respond to this by figuring out ways to change how the narrative is formed in the minds of everyone who is watching (which is pretty much everyone in the internet era) so that fewer people are receptive to extremist ideologies. Bombs and invasions are counterproductive here. We have to play the long game and respond to our adversaries' needs and desires as much as reasonably possible and move to a more fair and equitable treatment of them so that their societies can develop and promote ideas that fundamentally change the situation for the better. It's the only thing that will lead to a long term improvement in the situation, and it is the only approach that would be directly counteracting terrorist tactics.