Помогите разложить ** множители: (y-z)(y+z)^2+(z-x)(z+x)^2+(x-y)(x+y)^2

Question

Помогите разложить на множители: (y-z)(y+z)^2+(z-x)(z+x)^2+(x-y)(x+y)^2

Answer 1

(y-z)(y+z)^2+(z-x)(z+x)^2+(x-y)(x+y)^2=

(x^2-y^2)(x+y)+(y^2-z^2)(y+z)+(z^2-x^2)(z+x)=

x^3-xy^2+x^2y-y^3+y^3-z^2y-y^2z-z^3+z^3-x^2z-z^2x-x^3=

x^2y-x^2z-xy^2+xz^2+y^2z-yz^2=

xy(x-y)+z^2(x-y)-z(x^2-y^2)=

(x-y)(xy+z^2-z(x+y))=

(x-y)(xy+z^2-zx-zy)=

(x-y)(y(x-z)-z(x-z))=

(x-y)(x-z)(y-z)