4chan

That's exactly what eventually helped me understand it.

To multiply the negative by a negative is like an instruction to "reverse the circumstance that created the negative and then keep 'reversing' forward", so to speak.

You come across a hole in the ground. You see a shovel and 5 piles of dirt. That hole in the ground represents where that dirt used to be.

You can "add" more depth to the hole by digging, i.e. continuing to remove dirt and create more piles.

But you can also reverse what was done by "un-digging", I.e. putting the dirt back into the hole.

So if you "un-dug" the hole with the 5 piles of dirt, you'd have 0 piles, and 0 holes.

But if you "un-dug" the hole 5 times in a row, you've filled the hole and started creating a pile on top of it with dirt from somewhere else.