The HCF of (x 4 - y 4) and (x 6 - y 6) is

Let f (x) = (x⁴ - y⁴)
= (x² - y²) (x² + y²)
= (x - y) (x + y) (x² + y²)
and g(x) = (x⁶ - y⁶)
= (x³)² - (y³)²
= (x³ + y³) (x³ - y³)
= (x + y) (x² - xy + y²) (x - y)(x² + xy + y²)
= (x - y) (x + y) (x² - xy + y²)
(x² + xy + y²)
∴ HCF of [f(x), g(x)] = (x - y) (x + y)
= x² - y²