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Compute the expression below given that each number has 100 digits:

888...883 * 888...885 - 888...882 * 888...886

 Apr 3, 2021
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You can write this equation, given $x=888...883$, as $x(x+2)-(x-1)(x+3)=x^2+2x-(x^2-x+3x-3)=x^2+2x-(x^2+2x-3)=x^2-x^2+2x-2x+3$. Hey, it all cancels! We are left with $\boxed{3}$ (Note how this is true for all x, that $x(x+2)-(x-1)(x+3)=3$)

 Apr 3, 2021

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