Squaring numbers ending in 1

Here's a simple trick to square any number that ends in 1.
  •  Subtract 1 from the number.
  • Square the difference. (Squaring of such number is easy as it ends in ‘0’)
  • Add the difference twice to its square.
  • Add 1.
Example: If the number to be squared is 61  

1.    Subtract 1=> 61 - 1 = 60.
2.    Square the difference => 60 × 60 = 3600.
3.    Add the difference twice to its square => 3600 + 60 + 60 = 3720.
4.    Add 1 => 3720 + 1 = 3721.

Squaring-numbers-ending-in-1 So, 612 = 3721

812 =?

1)    81 - 1 = 80 (Subtract 1). 
2)    802 = 6400 (square the difference). 
3)    6400 + 80 + 80 = 6560 (add the difference twice to its square).
4)    6560 + 1 = 6561 (add 1)

So, 812 = 6561

If the number to be squared is a 3-digit number, let’s say 121

1)    121 - 1 = 120 (Subtract 1). 
2)    1202 = 14400 (square the difference). 
3)    14400 + 120 + 120 = 14640 (add the difference twice to its square).
4)    14640 + 1 = 14641 (add 1)

So, 1212 = 14641

2512 =?

1)    251 - 1 = 250  
2)    2502 = 62500 
3)    62500 + 250 + 250 = 63000
4)    63000 + 1 = 63001

So, 2512 = 63001


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