Multiplying two selected 3-digit numbers

steps

1. Select a 3-digit number with a middle digit of 0.
2. Choose a multiplier with the same first two digits, whose third digit sums to 10 with the third digit of the first 3-digit number.
3. The first digit(s) will be the square of the first digit:
   X _ _ _ _ or X X _ _ _ _.
4. The next digit will be the first digit of the numbers:
   _ X _ _ _ or _ _ X _ _ _.
5. The next digit is zero: _ _ 0 _ _ or _ _ _ 0 _ _.
6. The last two digits will be the product of the third digits:
   _ _ _ X X or _ _ _ _ X X.

Example:

1. If the first number is 407, choose 403 as the second number (same first digits, second digits add to 10).
2. 4 × 4 = 16 (square the first digit): 1 6 _ _ _ _.
3. The next digit will be the first digit of the numbers:
   _ _ 4 _ _ .
4. The next digit is zero: _ _ 0 _ _ .
5. 7 × 3 = 21 (the last two digits will be the product of the third digits: _ _ _ 2 1.
6. So 407 × 403 = 164021.

See the pattern?

1. If the first number is 201, choose 209 as the second number (same first digits, second digits add to 10).
2. 2 × 2 = 4 (square the first digit): 4 _ _ _ _.
3. The next digit will be the first digit of the numbers:
   _ 2 _ _ _ .
4. The next digit is zero: _ _ 0 _ _ .
5. 1 × 9 = 09 (the last two digits will be the product of the third digits: _ _ _ 0 9.
6. So 201 × 209 = 42009.