WASHINGTON (AP) — Mitt Romney ignored the most significant expansion of trade ties in nearly two decades when he accused the Obama administration Monday night of doing nothing to open new markets. Rick Santorum claimed to be taking purely the high road in campaign ads even as a new one from him veered from that path.

Newt Gingrich mischaracterized the Chilean retirement system that he favors as a partial model for the United States, declaring that the system of private accounts is voluntary when it's not.

So it went in the latest Republican presidential debate as the candidates took shortcuts with complex realities and committed some outright distortions. A look at some of the claims and how they compare with the facts:

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ROMNEY: "This president has opened up no new markets for American goods around the world in his three years, even as European nations and China have opened up 44."

THE FACTS: Actually, Obama revived Bush-administration-era free-trade pacts with South Korea, Panama and Columbia, all passed by Congress in October, in the biggest round of trade liberalization since the North American Free Trade Agreement and other pacts of that era.

In particular, the agreement with South Korea is designed to break down barriers between the United States and the world's 15th-largest economy. The South Korea deal has the potential to create as many as 280,000 American jobs, according to a recent assessment by the staff of the U.S. International Trade Commission, and to boost exports by more than $12 billion.

Obama also, on a recent trip to Asia, endorsed an Asia-Pacific free-trade pact that would also boost U.S. exports to Asia. With economies weak, the benefits of freer trade may not be immediate but Romney was incorrect to say President Barack Obama has opened "no new markets."

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SANTORUM: "My ads have been positive. The only ad that I've ever put up has contrasted myself with the other candidates, and does so in a way talking about issues."

THE FACTS: Santorum is coming out with an ad this week accusing Romney of being "just like Obama" and saying Romney "once bragged he's even more liberal than Ted Kennedy on social issues," two negative assertions that go beyond a mere look at issues.

As a Massachusetts senate candidate in 1994, Romney wrote to a group of gay Republicans that outlined a plan to do better than Kennedy to make "equality for gays and lesbians a mainstream concern." But that's not bragging about liberalism, and Romney is hardly more liberal than the late senator — or Obama — on social issues. Romney, for example, supports a constitutional amendment to ban gay marriage.

Santorum has, in fact, stayed positive in the campaign but the new ad is a departure from that.

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GINGRICH on Chile's system of private retirement accounts: "First of all, it's totally voluntary. If you want to stay in the current system, stay in it. If you are younger and you want to go and take a personal savings account, which would be a Social Security savings account, you can take it."

THE FACTS: There is nothing voluntary about Chile's system. It requires that all workers contribute 10 percent of their salaries to private pension plans, plus other fees for insurance, instead of a government program like Social Security.

Workers had a choice when Chile created the private pensions in 1981 but after that phase-in, all new employees have been required to contribute 10 percent of their first $33,360 in annual wages, choosing among five funds whose investments range from safe bonds to riskier stocks.

The Chile model was also a favorite of Herman Cain when he was in the Republican race. He, too, mischaracterized the system as optional.

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ROMNEY: "We invested in well over 100 different businesses. And the people have looked at the places that have added jobs and lost jobs and that record is pretty much available for people to take a close look at."

THE FACTS: Romney's record as a venture capitalist at Bain Capital has been presented by his campaign highly selectively; namely, by detailing several big success stories and ignoring the job losses that resulted from Bain-owned plants and companies that closed or shrank their workforce.

His overall record is not even close to being known, because it is so complex. Many of the companies are private, without the public disclosure requirements that big corporations have, and his campaign has not released details.

Under scrutiny, Romney has stepped back from claiming that he created more than 100,000 jobs overall with his Bain investments. That claim was never substantiated. In the debate, he named four successful investments in companies that now — a decade after he left Bain — employ about 120,000 people, a more measured and accurate statement, but one that still does not account for losses elsewhere.

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RON PAUL: "Taliban are people who want — their main goal is to keep foreigners off their land. It's the al-Qaida — you can't mix the two. The al-Qaida want to come here to kill us. The Taliban just says we don't want foreigners. We need to understand that or we can't resolve this problem in the Middle East."

THE FACTS: What Paul is missing is that the Taliban harbored foreigners in their land — al-Qaida terrorists who came to the United States and killed Americans— and that the Obama administration fears that might happen again if the Taliban regain control in Kabul.

He was correct that the U.S. prior to the 2001 terrorist attacks did not consider the Taliban to be a threat to the U.S. homeland.

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ROMNEY: "Three years into office, he doesn't have a jobs plan."

FACT CHECK: Like them or not, Obama has proposed several plans intended to spur the economy and create jobs. The most well-known was his stimulus plan, introduced in February 2009, which included about $800 billion in tax cuts and spending.

At the end of 2010, Obama struck a deal with GOP congressional leaders on a package intended to stimulate hiring and growth. The deal cut the Social Security payroll tax, which provided about an extra $1,000 a year to an average family. It also extended an unemployment benefits program that provided up to 99 weeks of aid.

And in September, Obama introduced his most recent jobs plan, rolling it out in a speech to the full Congress in which he urged Congress to "pass it right away." It included $450 billion in tax cuts and new spending, including greater cuts to payroll taxes and tax breaks for companies that hire those who've been out of work for six months or more. Almost none of it has been passed into law.

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GINGRICH: Romney "raised taxes."

ROMNEY: "We reduced taxes 19 times."

THE FACTS: Both assertions were basically true, though decidedly one-sided.

Romney largely held the line on tax increases but there were notable exceptions. The state raised business taxes by $140 million in one year with measures mostly recommended by Romney. As well, the Republican governor and Democratic lawmakers raised hundreds of millions of dollars from higher fees and fines — taxation by another name. Romney himself proposed raising nearly $60 million by creating 33 new fees and increasing 57 others. Romney won praise from anti-tax advocates by firmly backing income tax cuts — and criticism over the business taxes and fees.

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GINGRICH: "More people have been put on food stamps by Barack Obama than any president in American history."

THE FACTS: It's gotten easier to qualify for food stamps in the past decade but that is because of measures taken before Obama became president.

It's true that the number of people on food stamps is now at a record level. That's due mainly to the ailing economy, which Republicans blame on Obama, as well as rising food costs.

The worst downturn since the Great Depression wiped out 8.7 million jobs, pushed the unemployment rate to a peak of 10 percent in October 2009 and increased poverty.

More than 46.2 million people were on food stamps in October 2011, down slightly from a record 46.3 million in September. That's up from fewer than 31 million people three years earlier.

Eligibility rules were relaxed in 2002 and 2008 during the Bush administration. Obama's stimulus package, passed in February 2009, relaxed the program's work requirements through September 2010.