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!)
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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© Derek Cumberbatch