Multiplying 2 numbers together those differ by a small even number

If you’re good at memorizing some squares and use the tricks 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 12×14.

When two numbers differ by 2 their product is always the square of the number in between them minus 1.

12×14 = (13×13)-1 = 169-1 = 168.

16×18 = (17×17)-1 = 289-1 = 288.

99×101 = (100×100)-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.

11×15 = (13×13)-4 = 169-4 = 165.

13×17 = (15×15)-4 = 225-4 = 221.

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

12×18 = (15×15)-9 = 225-9 = 216.

17×23 = (20×20)-9 = 400-9 = 391.

This trick works effectively, if you’ve memorized or can quickly calculate the squares of numbers.