# 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) = x^{2} + x

x(x - 1) = x^{2} - 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: 101^{2} + 101 = 10,201 + 101 = 10,302

Method #2: 102^{2} - 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: 1^{2} - 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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© Derek Cumberbatch