Mitt Romney’s rivals this week intensified their attacks over business failures that happened on his watch at the investment firm Bain Capital. But even the successes touted by Romney’s campaign involved some painful decisions and layoffs.

Both the successes and the failures reveal the candidate’s faith in “creative destruction,” the notion that the new must relentlessly replace the old so that companies and the economy can become more efficient.

The concept is gospel to many businesspeople. But its intersection with politics has created what may be a recurring line of attack against Romney’s record.

Romney’s approach is visible in the three big Bain investments he trumpets in his official biography as evidence that he knows how to create jobs. The companies — Staples, Sports Authority and Domino’s Pizza — are well-known consumer brands, and the campaign has gone so far as to say that Romney helped create 100,000 jobs through his work related to those businesses.

But like Romney’s work on all the businesses Bain invested in, the primary goal with these companies wasn’t job creation but making them more profitable and valuable. This meant embracing aspects of capitalism that have unsettled some Americans: laying off workers when necessary, expanding overseas to chase profits and paying top executives significantly more than employees on lower rungs.

Supporters of Romney rival Newt Gingrich released a video on Wednesday accusing the former private-equity financier of laying off workers and profiting from the results. Yet Romney has never shied away from proclaiming his belief that job cuts are sometimes necessary.

The rise of Staples is in fact a textbook example of “creative destruction.”

Staples became a runaway business success in the 1980s and 1990s because it offered companies a smarter way of purchasing supplies, saving them money. As Staples grew, smaller stationery stores were shuttered. These losses are not counted in Romney’s jobs figure.

The rise of the company, which entered the Fortune 500 in 1996, has mirrored broader trends in corporate America, in which many multinational firms now see more potential growth abroad than in this country.

Staples, too, is steadily expanding overseas. In 2006, revenue outside North America accounted for 13 percent of revenue. In 2010, the share was 21 percent.

And as Staples has grown, so has the pay earned by its chief executive, from $4.7 million in 2006 to $10.8 million in 2010. The company explains in its annual report how it sets pay, saying that it uses comparable firms, such as Amazon, Best Buy and Starbucks, as benchmarks.

Staples does not disclose the wages of its 89,000 employees, nor does it break out how many work as retail associates. According to the Bureau of Labor Statistics, the mean annual wage of a retail salesperson in the United States is $25,000 a year.

Staples has not been immune from tough choices about cutting workers. During the depths of the recent recession, it laid off about 140 employees, half of whom worked at the company’s headquarters in Framingham, Mass.

When it has acquired companies, the firm has also had to lay off some workers — typical for any business acquisition.

In 2004, when Staples bought a small company called Hartford Office Supply, owned by two brothers, employees at the acquired firm worried about their jobs.

“We’re all devastated,” one worker told the Hartford Courant at the time. “This is one of the nicest, most family-oriented places that you could work . . . and I don’t know why they had to do this.”

Yet few would dispute that Staples has become a sterling American success story. From an idea hatched by entrepreneur Tom Stemberg, it has grown into a $24.5 billion company with 89,000 employees worldwide, all of whom Romney counts in his 100,000 job-creation total. Romney sat on the company’s board for more than a decade. Stemberg said in an interview that Romney was “the best single corporate director I’ve seen in action.”

Sports Authority and Domino’s have also grown tremendously since benefiting from Bain’s investments. But like Staples, they have had to lay off workers on occasion.

In March 2008, Domino’s announced that it was cutting roughly 50 employees after net quarterly earnings dropped 48 percent. It was the first time the company had done layoffs since 1999.

Sports Authority in 2003 merged with Gart Sports to become the country’s largest sporting-goods retailer. At the time, jobs were lost at Sports Authority’s headquarters in Fort Lauderdale, Fla., though some moved to the company’s new offices in Denver.

The Romney campaign says its candidate’s experiences at Staples, Sports Authority and Domino’s give him “the unique skills and capabilities to do what President Obama has failed to do: focus on job creation and turn around our nation’s faltering economy.”

But some private-equity experts think the link between Bain’s deals and jobs is more tenuous.

“I’ve got a lot of admiration for Bain Capital, but jobs were the byproduct of the mission, not the product,” said Howard Anderson, a senior lecturer at MIT’s Sloan School of Management. “The product was to increase wealth, and in some cases it meant expanding the company. In some cases it meant contracting the company.”

A Domino’s spokesperson said that the company “can’t put a number to the amount of jobs created since 1998,” the year Bain invested in the firm and began turning it around.

Anthony Carnevale, director of the Georgetown University Center on Education and the Workforce, said that despite job losses and other discomfiting changes when companies single-mindedly pursue profit, Americans are ultimately “believers in creative destruction.”

“Romney is mainstream in one sense, and that is that Americans are very committed to this process because we believe in the future and we believe in technology,” Carnevale said.