Multiplying together two numbers that differ by a small even number

This trick only works if you've memorized or can quickly calculate the squares of numbers. If you're able to memorize some squares and use the tricks described later for some kinds of numbers you'll be able to quickly multiply together many pairs of numbers that differ by 2, or 4, or 6.

Let's say you want to calculate 12x14.

When two numbers differ by two their product is always the square of the number in between them minus 1.

12x14 = (13x13)-1 = 168.

16x18 = (17x17)-1 = 288.

99x101 = (100x100)-1 = 10000-1 = 9999

If two numbers differ by 4 then their product is the square of the number in the middle (the average of the two numbers) minus 4.

11x15 = (13x13)-4 = 169-4 = 165.

13x17 = (15x15)-4 = 225-4 = 221.

If the two numbers differ by 6 then their product is the square of their average minus 9.

12x18 = (15x15)-9 = 216.

17x23 = (20x20)-9 = 391.

Posted in: Maths, Multiplication