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That's breast armor plates

The white breastplates on Vegeta's blue suit are part of the Saiyan armor that Vegeta wears. This armor is a standard battle gear worn by members of Frieza's army, including the Saiyans¹.

When Vegeta's armor and bodysuit were damaged in battle against Recoome, he replaced his outfit with an older model design. This design consisted of a navy-blue bodysuit, white gloves and boots, and white armor with brown plates on the stomach and lower back¹. The white breastplates you're referring to are part of this armor.

The armor, including the breastplates, is designed to be highly flexible and durable. It can stretch to fit the wearer's body shape². This is particularly useful for Saiyans who have the ability to transform into Oozarus, significantly increasing their size².

It's also worth noting that unlike the original design of King Vegeta, Vegeta's design doesn't possess the Saiyan Royal Family crest in the left chest plate of his armor³. This could be seen as a symbol of Vegeta's complex relationship with his royal heritage and his own personal journey.

Overall, the armor, including the breastplates, is a visual representation of Vegeta's character and status. Despite the changes in his armor throughout the series, the basic design remains the same, symbolizing Vegeta's pride in his Saiyan heritage¹.

Source: Conversation with Bing, 11/8/2023 (1) Vegeta | Dragon Ball Wiki | Fandom. https://dragonball.fandom.com/wiki/Vegeta. (2) 15 Facts You Probably Didn't Know About Dragon Ball Z's Vegeta - Twinfinite. https://twinfinite.net/gallery/15-facts-about-dragon-ball-z-vegeta/. (3) King Vegeta | Dragon Ball Wiki | Fandom. https://dragonball.fandom.com/wiki/King_Vegeta. (4) Fashion Ball Z: 15 Of Vegeta's Biggest Looks, Ranked - CBR. https://www.cbr.com/dragon-ball-z-vegetas-best-looks-ranked/.