Beauty of Maths!
 
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