Evaluate the product without multiplying directly: 103 107 - Vidyadip

Question

Evaluate the product without multiplying directly: $103 \times 107$

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Answer

$103 \times 107$
$103 \times 107$ can also be written as $(100+3)(100+7)$.
We can observe that we can apply the identity $(x+a)(x+b)=x^2+(a+b) x+a b$
$(100+3)(100+7)=(100)^2+(3+7)(100)+3 \times 7$
$=10000+1000+21$
$=11021$
Therefore, we conclude that the value of the product $103 \times 107$ is $11021 .$

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