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