“I look better if I’m worth $10 billion than if I’m worth $4 billion,” he once said when disputing his ranking on the Forbes billionaires list. In a court case, he acknowledged that when it came to describing the value of his brand, “I’m as accurate as I think I can be.” And when he described his self-aggrandizing style in his book, “The Art of the Deal,” he chose a phrase that has followed him ever since: “truthful hyperbole.”’

But now, Mr. Trump will face questions under oath about that pattern of embellishment in an investigation that may shape the future of his family real estate business. The former president and his eldest daughter, Ivanka Trump, are expected to be questioned later this month by the New York State attorney general’s office, which has been conducting a civil investigation into whether he and his company fraudulently inflated the value of his assets. His son, Donald Trump Jr., was interviewed last week, according to people with knowledge of the matter.

The attorney general, Letitia James, has argued in court papers that “fraudulent or misleading” business practices reigned at the Trump Organization for years, and has said her investigators must question the Trumps to determine who was responsible. Mr. Trump fought hard to avoid an interview, but a judge ordered him to face questioning, and investigators will seek to elicit answers that might reveal whether he approved any bogus valuations of his hotels, golf clubs and other assets.