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**Prove It** Draw yourself a 10 x 10 grid.

Say you wanted to find out what 9 x 9 is...

It might make sense to start with 10 x 10, and then take away one whole row of 10 and one whole column of 10 (so you are left with the 9 x 9 grid)...

The problem with taking one row of 10 and one column of 10 is that you've taken away 1 too many (you've taken away the one in the corner twice). So you have to add it back on...

What we have shown is a pictorial representation of the distributive law...

9 x 9 = (10 - 1) x (10 - 1)

= (10 x 10) - (10 x 1) - (1 x 10) - 1 x (-1)

But the only way that this makes sense is if the -1 x -1 = + 1.

= (10 x 10) - (10 x 1) - (1 x 10) + 1.

Therefore, negative times negative is positive.