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103*97=103(100-3)=10300-309=9991.

Multiply the product 103*97 in your head.

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$(a+b)(a-b)=a^2-b^2$

$(100+3)\times (100-3)=10000-9=9991$

This can easily be calculated in the head.

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so it becomes 100*97+3*97=9700+97+97+97=9700+291=9911