Question

Помогите, плиз))
Докажите тождество:
(х³-у³)²+2х³у³=(х²+у²)(х⁴+у⁴-х²у²)

Answer 1

$(x^3-y^3)^2+2x^3y^3=(x^3)^2-2x^3y^3+(y^3)^2+2x^3y^3=x^6+y^6=\\\\=(x^2)^3+(y^2)^3=(x^2+y^2)((x^2)^2-x^2y^2+(y^2)^2)=\\\\=(x^2+y^2)(x^4-x^2y^2+y^4)$