Using $(x + a) (x + b) = x^{2} + (a + b) x + a b$ , find $103 x 98$

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Solution

$103 x 98$ can be written as $(100 + 3) (100 + (- 2)$
$= 103 x 98 = (100 + 3) (100 + (- 2)$
Using $(x + a) (x + b) = x^{2} + (a + b) x + a b$
Putting
$x = 100, a = 3, b = - 2$
$= (100 + 3) [(100 + (- 2)] = 100^{2} + [3 + (- 2)] 100 - 6$
$= (100 + 3) (100 + (- 2)) = 10000 + 1 \times 100 - 6$
$= (100 + 3) (100 + (- 2)) = 10000 + 100 - 6$
$= (100 + 3) (100 + (- 2)) = 10094$
$= 103 x 98 = 10094$
Hence, the required answer is $10094$

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