What is the value of 9991 × 10009?
99999919
Write the factors symmetrically about 10000:
\[9991\times 10009=(10000-9)(10000+9)\]
Apply the difference-of-squares identity \((a-b)(a+b)=a^2-b^2\):
\[=10000^2-9^2=100000000-81=99999919\]
Therefore the product is 99999919.
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