(Х-1)(х+1)(х^2+1)(х^4+1)(х-1)(х+1)(х^2+1)(х^4+1) при х=2

Question

(Х-1)(х+1)(х^2+1)(х^4+1)(х-1)(х+1)(х^2+1)(х^4+1) при х=2

Answer 1

(x - 1)(x + 1)(x² + 1)(x⁴ + 1)(x - 1)(x + 1)(x² + 1)(x⁴ + 1) = ((x - 1)(x + 1)(x² + 1)(x⁴ + 1))² = ((x² - 1)(x² + 1)(x⁴ + 1))² = ((x⁴ - 1)(x⁴ + 1))² = (x⁸ - 1)²
При x = 2:
(x⁸ - 1)² = (2⁸ - 1)² = (256 - 1)² = 255² = 65025.