Squaring a 2-digit number ending in 1

1. Take a 2-digit number ending in 1.
2. Subtract 1 from the number.
3. Square the difference.
4. Add the difference twice to its square.
5. Add 1.

Example:

1. If the number is 41, subtract 1: 41 - 1 = 40.
2. 40 × 40 = 1600 (square the difference).
3. 1600 + 40 + 40 = 1680 (add the difference twice
   to its square).
4. 1680 + 1 = 1681 (add 1).
5. So 41 × 41 = 1681.

See the pattern?

1. For 71 × 71, subtract 1: 71 - 1 = 70.
2. 70 × 70 = 4900 (square the difference).
3. 4900 + 70 + 70 = 5040 (add the difference twice
   to its square).
4. 5040 + 1 = 5041 (add 1).
5. So 71 × 71 = 5041.

Posted in: Mathematics Tips,Squaring Numbers,Tricky mathematics