Short cut cubing of any two digit number just in few seconds with help of algebraic identity

We can utilize following algebraic identity to easily find cube of any two digit number

A³ = (A - d) x A x (A + d) + d² x A

Where, d = any assumed value to easily compute cube.

Naturally, this formula works for any value of d, but we choose d to be the distance to a number close to A that is easy to multiply.
For example,

To find cube of the number 23,

Let, d = 3, A = 23

So,

A³ = (A - d) x A x (A + d) + d² x A

= (23 - 3) x 23 x (23 + 3) + (3)² x 23

= 20 x 23 x 26 + (3)² x 23

= 20 x 598 + 9 x 23

= 11960 + 207

= 12167

Quick multiplication of any two digit number near to each other with help of algebraic close together method

We can utilize following algebraic identity for quick multiplication of any two digit number which are near to each other

(z + a) x (z + b) = z x (z + a + b) + a x b

Where, z = any number ends with zero.

For example,

To multiply 23 x 26,

Let, z = 20, a = 3, b = 6

So, 

(z + a) x (z + b) 

= z x (z + a + b) + a x b

= 20 x (20 + 3 + 6) + 3 x 6

= 20 x 29 + 3 x 6

= 580 + 18

= 598

Another example,

To multiply 88 x 86,

Let, z = 80, a = 8, b = 6

So, 

(z + a) x (z + b) 

= z x (z + a + b) + a x b

= 80 x (80 + 8 + 6) + 8 x 6

= 80 x 94 + 8 x 6

= 7520 + 48

= 7568

Short cut squaring of any three digit number just in few seconds with help of algebraic identity

We can utilize following algebraic identity to easily find square of any three digit number

A² = (A - d) x (A + d) + d²

Where, d = any assumed value to easily compute square.

We can quickly square three-digit numbers by rounding up and down to the nearest hundred. 
For example,

To find square of the number 223,

Let, d = 23, A = 223

So,

A² = (A - d) x (A + d) + d²

= (223 - 23) x (223 + 23) + (23)²

= 200 x 246 + 529

= 49200 + 529

             = 49729

Short cut squaring of any two digit number just in few seconds with help of algebraic identity

We can utilize following algebraic identity to easily find square of any two digit number

A² = (A - d) x (A + d) + d²

Where, d = any assumed value to easily compute square.

Naturally, this formula works for any value of d, but we choose d to be the distance to a number close to A that is easy to multiply. 
For example,

To find square of the number 23,

Let, d = 3, A = 23

So,

A² = (A - d) x (A + d) + d²

= (23 - 3) x (23 + 3) + (3)²

= 20 x 26 + 9

= 520 + 9

= 529

Another example,

To find square of the number 48,

Let, d = 2, A = 48

So,

A2 = (A - d) x (A + d) + d²

= (48 - 2) x (48 + 2) + (2)²

= 46 x 50 + 4

= 2300 + 4

= 2304