Multiplying two numbers that differ from a number by the same small number
Follow the following examples to understand the simple idea behind it.
Example 1:
99 * 101 = (100 - 1) * (100 + 1) = (100 * 100) - 1 = 10000 - 1 = 9999
Rem:
99 * 101 = (100 * 100) - (1 * 1)
Example 2:
997 * 1003 = (1000 - 3) * (1000 + 3) = (1000 * 1000) - (3 * 3) = 1000000 - 9 = 999991
Rem:
997 * 1003 = (1000 * 1000) - (3 * 3)
Example 3:
47 * 53 = (50 - 3) * (50 + 3) = 2500 - 9 = 2491
Rem:
47 * 53 = (50 * 50) - (3 * 3)
Example 4:
195 * 205 = (200 * 200) - (5 * 5) = 39975