There's still a lot we don't know about Google's upcoming Android P release, but thanks to an inadvertent leak on Google's own blog, speculation about certain minor details has now exploded. It looks like the Home button icon has turned into a pill, the back button into an outline, and the dialog boxes now have curved edges.
In a blog post talking about network security improvements in Android P, a screenshot left in tact revealed all of the things mentioned above, as well as a couple of other aesthetic changes. Since publishing, Google cropped out some of the screenshot, which could either mean we were simply not meant to see those details yet, or, it could mean that it's not final design, and could change. This is what speculation is all about.
At the bottom of the screenshot, we can see the home button replaced with a solid pill icon, and the back button has been turned into an outline. At the same time, the multi-tasking button has been removed, and that's leading to even more speculation. The back button is said to be context-aware, so it only appears if it's actually needed. In this case of a dialog, the back button would simply close it, acting as a "cancel". It could be, then, that the multitasking button hasn't been removed, but simply isn't required in this shot when only a single app is open (we can't tell from the screenshot, however, so this is again another assumption).
If Google did get rid of the multitasking button, it's likely to be because the company copied an Apple iOS-like gesture and will let people access their open apps by swiping up from the bottom of the screen. In many ways, this could be easier than current solutions, especially those that hide the buttons by default, making you tap the screen (or swipe up) first to see the icons, and then tap the multitasking button. It seems easier to simply swipe up, and instantly have the list available.
Again, this is all speculation at this point, but considering the fact that this screenshot came straight from Google itself does instill a lot more faith in the likelihood of changes, rather than if it showed up from a random leaker.