[ Formulas for abbreviated multiplication (other).]

Calculate: $\frac{(2001 \cdot 2021+100)(1991 \cdot 2031+400)}{2011^{4}}$
$2001 \cdot 2021+100=(2011-10)(2011+10)+100=2011^{2}-10^{2}+100=2011^{2}, 1991 \cdot 2031=2011^{2}-20^{2}+400=$ 20112. Thus, the numerator is equal to the denominator.

## Answer

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