Докажите тождество (x+5)(x-5)(x^2+5x+25)(x^2-5x+25)=x^6-5^6

Question

Алгебра: Докажите тождество (x+5)(x-5)(x^2+5x+25)(x^2-5x+25)=x^6-5^6

hamestik · Answer

(x + 5)(x - 5)(x² + 5x + 25)(x² - 5x + 25) = x⁶ - 5⁶

(x + 5)(x - 5)(x² + 5x + 25)(x² - 5x + 25) = (x³ - 5³)(x³ + 5³)

(x + 5)(x² - 5x + 25)(x - 5)(x² + 5x + 25) = (x³ - 5³)(x³ + 5³)

(x³ + 5³)(x³ - 5³) = (x³ - 5³)(x³ + 5³)