Evaluate the following products without multiplying directly.
$103 \times 97$

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Solution

$103 \times 97 = (100 + 3) (100 - 3)$
Using identity
$(a + b) (a - b) = a^{2} - b^{2},$ we get
$103 \times 97 = (100)^{2} - (3)^{2}$
$= 10000 - 9 = 9991$

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