Question

Evaluate the following product using suitable identity: 392x508

Answer 1

$\frac{508 + 392}{2} = \frac{900}{2} = 450 \\ \\ \frac{508 - 392}{2} = \frac{116}{2} = 58 \\ \\ 392 * 508 = (450 - 58)(450 + 58) \\ = 450^2 - 58^2 = 202500 - 3364 = 199136$

OR

$392 * 508 = (400 - 8)(500 + 8) \\ = (400 * 500) + (400 * 8) + (-8 * 500) + (-8 * 8) \\ = 200000 + 3200 + (- 4000) + (- 64) \\ = 200000 + 3200 - 4000 - 64 = 199136$

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