Consecutive Integer Multiplication

If you multiply sets of consecutive integers in a list, (2 at a time) something special can happen!

Brain saying "WOW!"

Multiplied Integers	Products	Differences of the Products(Absolute Value)
0×1	0	2
1×2	2	4
2×3	6	6
3×4	12	8
4×5	20	10
5×6	30	12
6×7	42	14
7×8	56	16
8×9	72	18
9×10	90	20
10×11	110	22
11×12	132	24
12×13	156	26
13×14	182

The differences of the products are consecutive even numbers!

The trick still works if you include negative numbers, but...

Multiplied Integers	Products	Differences of the Products(Absolute Value)
-5×-4	20	8
-4×-3	12	6
-3×-2	6	4
-2×-1	2	2
-1×0	0	0
0×1	0	2
1×2	2	4
2×3	6	6
3×4	12	8
4×5	20

You can get a palindrome in the products' & differences' columns!

Multiplying 2 negative numbers (real ones only) gives you a positive product; for the product to be negative, the 2 numbers must have different signs.

Note: Remember that absolute value is always positive, so that subtracting bigger numbers from smaller numbers won't give you a negative number. You should already know that the answer to a subtraction problem is called a difference.

There's a quadratic function to consider for this math trick:

Y = X^2 + X

X = Smaller integer

Y = Product of both integers

Multiplying x by (x + 1) simply gives you x² + x.

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© Derek Cumberbatch