Using $(x + a) (x + b) = x^{2} + (a + b) x + a b$ , find $(5.1 x 5.2)$

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Solution

$5.1 x 5.2$ can be written as $(5 + 0.1) (5 + 0.2)$
$= 5.1 x 5.2 = (5 + 0.1) \times (5 + 0.2)$
Using $(x + a) (x + b) = x^{2} + (a + b) x + a b$
$(5 + 0.1) (5 + 0.2) = 5^{2} + (0.1 + 0.2) \times 5 + (0.1 x 0.2)$
$= 5^{2} + (0.1 + 0.2) \times 5 + (0.1 x 0.2)$
$= 25 + (0.3 \times 5) + 0.02$
$= 25 + 1.5 + 0.02$
$= 26.52$
Hence, $5.1 x 5.2 = 26.52$ .

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