let
n = a x 10 + b ; First Two-Digit Number
r = c x 10 + d ; Second Two-Digit Number
If
a = c
b + d = 10
Then
n x r = (a x 10 + b ) x (c x 10 + d)
n x r = a x c x 100 + (a x d + b x c) x 10 + b x d
where
a = c
b + d = 10 >>> d = 10 - b
n x r = a x a x 100 + (a x (10 - b)+ b x a) x 10 + b x d
n x r = a x a x 100 + (a x 10 - b x a + b x a) x 10 + b x d
n x r = a x a x 100 + a x 100 + b x d
n x r = a x (a + 1 )x 100 + b x d
example
44 x 46 = (4 x 5 x 100 = 2000) + (4 x 6 = 24) = 2024
52 x 58 = (5 x 6 x 100 = 3000) + (2 x 8 = 16) = 3016
78 x 72 = (7 x 8 x 100 = 5600) + (8 x 2 = 16) = 5616
91 x 99 = (9 x 10 x 100 = 9000) + (9 x 1 = 9) = 9009