2 Quick Multiplication Methods!

There are 2 quick methods you can use to multiply numbers, but they only work when the 2 numbers (the multiplier & the multiplicand) have a difference of 1 in absolute value.

These 2 familiar binomial expansions should give you an idea:

x(x + 1) = x² + x

x(x - 1) = x² - x

(You must have seen these many times in your algebra classes!)

Anyway, you can either add the smaller number to its square or subtract the bigger number from its square to get the product of both numbers if & only if their difference is |1|!

Example:

101 × 102

Method #1: 101² + 101 = 10,201 + 101 = 10,302

Method #2: 102² - 102 = 10,404 - 102 = 10,302

101 × 102 = 10,302

Here's what happens if their difference is NOT equal to |1|:

1/2 × 1

Method #1: (1/2)² + 1/2 = 1/4 + 1/2 = 3/4

Method #2: 1² - 1 = 1 - 1 = 0

3/4 ≠ 0; 1/2 × 1 = 1/2

This math trick works with non-integers also; however, the multiplier & the multiplicand still need to have a difference of |1|; otherwise, neither of the 2 methods of this math trick will work. This math trick also works with SOME imaginary/complex numbers.

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