Multiplying Two Numbers Equidistant from a Third Number

This trick uses the difference of squares formula, $(x-d)(x+d) = x^2 - d^2$. It's useful for multiplying two numbers that are equally spaced from a convenient middle number (usually a multiple of 10 or 5).

Procedure:

• Find the middle number between the two numbers being multiplied and square it.
• Find the difference between the middle number and one of the original numbers, and square that difference.
• Subtract the second result from the first.

For example, $83 \times 87$. The middle number is 85, and the distance is 2. The calculation is $85^2 - 2^2 = 7225 - 4 = 7221$.