Expanding the expression:

(x² - 5x + 7)² = (x² - 5x + 7)(x² - 5x + 7)
= x⁴ - 5x³ + 7x² - 5x³ + 25x² - 35x + 7x² - 35x + 49
= x⁴ - 10x³ + 39x² - 70x + 49

Now subtracting 2(x² - 5x + 7):

2(x² - 5x + 7) = 2x² - 10x + 14

Now subtracting 3:

(x² - 5x + 7)² - 2(x² - 5x + 7) - 3 = x⁴ - 10x³ + 39x² - 70x + 49 - 2x² + 10x - 14 - 3
= x⁴ - 10x³ + 39x² - 70x + 49 - 2x² + 10x - 17
= x⁴ - 10x³ + 37x² - 60x + 32