Belgian investigators are starting to piece together how a cell of Islamic State operatives managed to build at least three bombs and kill at least 31 people in a city that has been on high alert since the Paris attacks last fall.

Police have found a peroxide-based explosive known as triacetone triperoxide, or TATP, in the apartment of one of the suspected bombers, although investigators have yet to say conclusively what type of devices were used Tuesday. But if TATP was the primary ingredient in the bombs, the attack in Brussels would become the latest example of the chemical’s use in terrorist strikes across Europe.

Highly unstable, peroxide-based explosives such as TATP — and its sibling hexamethylene triperoxide diamine, or HMTD — have been used in terrorist bombs for decades. TATP first gained notoriety after the Sept. 11, 2001, attacks when Richard Reid, who became known as the shoe bomber, unsuccessfully tried to detonate a TATP-triggered explosive during a Paris to Miami flight in December 2001.

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TATP was again used in the 2005 London bombings that killed 56 and was also confiscated from Najibullah Zazi in his failed plot to attack the New York City subway system in 2009. In the November 2015 attacks in Paris, TATP was used as the primary explosive in a number of bombs and suicide belts during the hours-long siege.

The chemicals that make up TATP, such as concentrated hydrogen peroxide and acetone, are easy to procure. There were 40 gallons of acetone in the apartment of the suspected bomber. The attackers in Brussels could have purchased the ingredients without raising suspicion, especially if each member was responsible for buying just one element.

When cooked, the white powdery substance is highly volatile and potent, earning it the nickname “The Mother of Satan.” A few grams of TATP can easily blow off fingers, while concentrated pounds of it are devastating.

According to an Army explosive ordnance disposal technician, who requested anonymity because he is not authorized to speak to the press, TATP-based devices are rarely seen in war zones such as Iraq and Afghanistan because of how unstable the material is and because military-grade explosives are readily available. TATP, he said, has become a terrorist staple in Europe because of its easily obtained ingredients.

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According to Brian Castner, a former Air Force explosive ordnance disposal technician and author of the book “All the Ways We Kill and Die,” the use of TATP-based explosives in both Paris and Brussels could suggest that a terrorist network in Europe has mastered the cooking and handling of TATP. “There are actually very few bombmakers in the grand scheme of things,” Castner said. “Once one finds a successful way to construct these things, they [can] mass produce.”

While there are bomb-building manuals available on the Internet, Castner added that a competent terrorist cell would not rely on them; instead, recruits apprentice with master bombmakers in places such as Syria and Iraq before returning to their home countries. And in Afghanistan and Iraq, the United States has targeted bombmakers. In 2008, for instance, a drone strike in Pakistan killed Abu Khabab al-Masri, who trained a generation of al-Qaeda operatives in bombmaking. Israel has similarly targeted bombmakers in Hamas.

According to Belgian media reports, the suspected bombmaker involved in Tuesday’s attacks is 24-year-old Najim Laachraoui, whose DNA was also found on some of the bombs used in the Paris attacks. He is believed to have trained in Syria. It is highly unusual for bombmakers to participate directly in operations, but The Post reported Wednesday that Laachraoui was the second suicide bomber at the airport, and he may have been willing to die because he feared the police were closing in.

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Some reports indicate that the bombs at the airport were detonated within suitcases, while a suicide vest may have been used in the Metro bombing.

While a seemingly small distinction, the two delivery methods involve different kinds of construction for the bombmaker. A TATP-loaded vest is harder to build and maintain, as the substance is so volatile. A suitcase loaded with TATP would be easier to transport and less likely to accidentally explode, since the charges would be more protected than if placed in a vest.

Pictures posted online of three suspects pushing carts loaded with suitcases through Brussels Airport show two of them wearing black gloves on their left hands. According to the Army technician, the gloves could have hidden triggering devices for the bombs.

This post has been updated