WASHINGTON — Four years ago he was the fifth-youngest president to take the oath of office. Now Barack Obama is 51, his hair more gray, his face more lined.

He’s the parent of a teenager and a tween. (Insert your own joke about teens and gray hair here.) His blood pressure has ticked up a bit, although it’s still excellent. He’s quit smoking. He’s a pet owner.

And the changes in the president aren’t just physical. As he enters Term Two, he is sounding more confident, vowing a harder line on negotiations, relying more on trusted allies, promising less and expressing more cynicism about the grip of partisanship on Washington.

And perhaps most important, he seems more convinced of a need to keep the public with him, coming full circle to his people-driven 2008 campaign.

“You can’t change Washington from the inside,” he said during his re-election campaign. “You can only change it from the outside.”

On the best days of his presidency, Obama has been witness to the power and possibilities of the office he holds. On the worst, he’s seen its limitations.

He has celebrated passage of his mammoth health-care overhaul. And mourned the lost children of Newtown.

He has savored the nail-biter news that Osama bin Laden at last had been brought down. And stood vigil over the remains of fallen soldiers returned to Dover, Del.

Between the highs and lows came the daily grind of a daunting job whose demands never end. There is always one more negotiation. One more legislative tussle. One more economic soft spot. One more natural disaster.

By all accounts, Obama’s style and his character remain largely unchanged. But every chapter of his presidency — the gasp-inducing early economic crisis, the battle over health care, the midterm congressional shellacking, the mass shootings in the past year, the endless negotiations over debt and deficit, the re-election brawl — has helped to mold him and to shape his perspective.

“Four years in, he has a very good sense of the job,” says senior adviser Valerie Jarrett. “He has a great sense of what is possible if you do have the American people behind you and willing to push with you to make change.”

The president himself, in remarks here and there, has laid out plenty of first-term takeaways that reflect the difficulties he’s faced:

n “Everything takes a little longer than you’d like.”

n “I underestimated the degree to which, in this town, politics trumps problem solving.”

n “The mistake of my first couple of years was thinking that this job was just about getting the policy right.”

n “No choice you make is without costs.”

n “We’ve got to break the habit of negotiating through crisis over and over again.”

To be sure, there’s a large dose of self-exoneration in the lessons Obama has taken from the job, as if he had little hand in Washington’s obstinacy and all the scheming political operatives are on the other side.

Republicans largely blame wrong-headed presidential policies and unyielding tactics. And some in the president’s own party wonder whether his new, tougher rhetoric truly will result in firmer stands.

“He hasn’t changed nearly as much as either Democrats or Republicans wish,” says Calvin Jillson, a political scientist at Southern Methodist University.

The public, for its part, has revised its own assessment of Obama over the past four years.

Polls show the president is still regarded as a good communicator, friendly, well-informed, caring, trustworthy. But there’s been a significant slide in the share who see him as a strong leader and as someone who can get things done.

Andrew Kohut of the Pew Research Center thinks Obama’s numbers on that count are due to rebound somewhat, given recent improvement in his approval ratings. His approval numbers are back in the mid-50s after dipping into the 40s at times in 2011 and 2012. But they’re still nowhere near the 60s and 70s of his first few months in office.

The president himself came out of his re-election victory convinced he has a stronger hand, and eager to use it before power inevitably ebbs later in his second term. He says he won’t negotiate with Republicans on raising the debt limit. He’s used his executive powers to act unilaterally to try to reduce gun violence.

That emboldened re-election outlook is coupled with a determination to stay above the day-to-day fighting and to keep the public with him.

In announcing a package of proposals this week to reduce gun violence, the president did what he could on his own, but also acknowledged that the most important provisions require congressional approval, and said it would take a demanding public to make that happen.

“His audience has become much more the American people than the people who live within the confines of Washington,” says former Obama spokeswoman Jennifer Psaki.

The Brookings Institution’s William Galston, who served in the Clinton White House, says Obama seems to have concluded that “getting into the weeds is a mistake.”

The way he handled the latest negotiations over taxes “might be seen as a new paradigm,” Galston says. “The president is not spending a lot of time with his sleeves rolled up, face to face with people who disagree with him.”

Nor is he making as many promises. After making more than 500 specific promises in his first campaign — more of them kept than broken — the president served up far fewer re-election pledges and has displayed a more measured view of what’s possible.

He’s a “happy warrior” the president says of himself, but he also admits to disappointment that he hasn’t gotten more cooperation from Congress.

Some liberals who complained that the president wasn’t tough enough in the first term look at his recent decision to give more ground than expected in extending Bush-era tax cuts to some wealthier Americans and wonder if he’s really stiffened his spine for term two.

“The guy can’t seem to help himself,” says Norman Solomon, an activist on the left. “He swears off caving in like some people swear off smoking, and the next day you see another lethal product in his mouth.”

The president’s renewed determination to leverage public support appears to be coupled with a willingness by the no-drama president to show more emotion when matters of public policy are also personal to him.

Hours after the massacre of 20 children in Newtown, Conn., a tearful Obama showed raw grief in his first comments on the attack. His temper flared after Republicans criticized U.N. Ambassador Susan Rice over the deaths of four Americans during an attack on a U.S. Consulate in Libya, insisting her critics “should go after me” instead.

There’s been less drama, though, within the president’s staff. Former aides who describe the early years of his presidency as marked by personnel disagreements and internal strife say that dynamic has given way to a more cohesive Obama team with time.

There’s been recent concern that the president’s early choices for his second-term Cabinet and top advisers are less diverse than past personnel picks, and that he and his team are too insular. Give it time, says Obama, insisting he’ll build a well-rounded team.