Using $(x + a) (x + b) = x^{2} + (a + b) x + a b$ , find $(103 x 104)$

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Solution

$103 x 104$ can be written as $(100 + 3) \times (100 + 4)$
Using $(x + a) (x + b) = x^{2} + (a + b) x + a b$
$= (100 + 3) (100 + 4) = 100^{2} + (3 + 4) \times 100 + 12$
$= (100 + 3) (100 + 4) = 10000 + 7 \times 100 + 12$
$= (100 + 3) (100 + 4) = 10000 + 700 + 12$
$= (100 + 3) (100 + 4) = 10712$
$= 103 x 104 = 10712$
Hence, the value of $103 x 104$ is $10712 .$

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