maths magic

> 1 x 8 + 1 = 9
> 12 x 8 + 2 = 98
> 123 x 8 + 3 = 987
> 1234 x 8 + 4 = 9876
> 12345 x 8 + 5 = 98765
> 123456 x 8 + 6 = 987654
> 1234567 x 8 + 7 = 9876543
> 12345678 x 8 + 8 = 98765432
> 123456789 x 8 + 9 = 987654321
>
> 1 x 9 + 2 = 11
> 12 x 9 + 3 = 111
> 123 x 9 + 4 = 1111
> 1234 x 9 + 5 = 11111
> 12345 x 9 + 6 = 111111
> 123456 x 9 + 7 = 1111111
> 1234567 x 9 + 8 = 11111111
> 12345678 x 9 + 9 = 111111111
> 123456789 x 9 +10= 1111111111
>
> 9 x 9 + 7 = 88
> 98 x 9 + 6 = 888
> 987 x 9 + 5 = 8888
> 9876 x 9 + 4 = 88888
> 98765 x 9 + 3 = 888888
> 987654 x 9 + 2 = 8888888
> 9876543 x 9 + 1 = 88888888
> 98765432 x 9 + 0 = 888888888
>
> Brilliant, isn't it?
>
> And finally, take a look at this symmetry:
>
> 1 x 1 = 1
> 11 x 11 = 121
> 111 x 111 = 12321
> 1111 x 1111 = 1234321
> 11111 x 11111 = 123454321
> 111111 x 111111 = 12345654321
> 1111111 x 1111111 = 1234567654321
> 11111111 x 11111111 = 123456787654321
> 111111111 x 111111111=123456789 87654321