Product of sum by difference application

Submitted by Isoscel on Tue, 01/15/2008 - 07:27.

We know the formula

$x^2-y^2=(x-y)(x+y)$

This formula gives us opportunity to find some product .
First we prepare ourselves to apply former formula in the opposite direction.

$(x-y)(x+y)=x^2-y^2$

$19*21=(20-1)(20+1)=20^2-1=400-1=399$
$29*31=(30-1)(30+1)=30^2-1=900-1=899$
$39*41=(40-1)(40+1)=40^2-1=1600-1=1599$
$49*51=(50-1)(50+1)=50^2-1=2500-1=2499$

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Product of sum by difference application