Formulas :

First 2 digits = [ __ x ( __ + 1 )]

Last 2 digits = __ x __

Example :

37 x 44

First 2 digits = [4 × ( 3 + 1 )]

= 16

Last 2 digits = 7 × 4

= 28

So, 37 × 44 = 1628

Formulas :

__( __ + __ )__²

Example :

107²

1( 7 + 7 )7²

11449

So, 107² = 11449

Formulas :

100 − __ = __  

First 2 digits = 100 − ( __ + __ )

Last 2 digits = __²

Example :

98²

100 − 98 = 2

First 2 digits = 100 − ( 2 + 2 )

= 100 − 4

= 96

Last 2 digits = 2²

= 4

So, 98² = 9604

Formulas :

add 0 at the start and end of the number.

Example :

12 x 314 = 03140

Divide them to 2 in a group.

(0 x 2) + 3 = 3

(3 x 2) + 1 = 7

(1 x 2) + 4 = 6

(4 x 2) + 0 = 8

So, 12 x 314 = 3768

Formulas :

( __ x __ )[( __ x __ ) + ( __ x __ )][( __ x __ ) + ( __ x __ )]( __ x __ )

Example :

121 × 23

( 1 x 2 )[( 1 x 3 ) + ( 2 x 2 )][( 2 x 3 ) + ( 1 x 2 )]( 1 x 3 )

(2)(3 + 4)(6 + 2)(3)

(2)(7)(8)(3)

So, 121 × 23 = 2783

Formulas :

( __ x __ )[( __ x __ ) + ( __ x __ )][( __ x __ ) + ( __ x __ ) + ( __ x __ )][( __ x __ ) + ( __ x __ )]( __ x __ )

Example :

121 x 310

( 1 x 3 )[( 1 x 1 ) + ( 2 x 3 )][( 1 x 0 ) + ( 2 x 1 ) + ( 1 x 3 )][( 2 x 0 ) + ( 1 x 1 )]( 1 x 0 )

(3)(1 + 6)(0 + 2 + 3)(0 + 1)(0)

(3)(7)(5)(1)(0)

So, 121 × 310 = 37510