Докажите тождность x^6-y^6=(x-y)(x+y)(x^2-xy+y^2)(x^2+xy+y^2)

Question

Докажите тождность
x^6-y^6=(x-y)(x+y)(x^2-xy+y^2)(x^2+xy+y^2)

Answer 1

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)