因式分解x^3-y^3+8z^3+6xyz阅读：a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-ac-bc)根据上面提示分解因式x^3-y^3+8z^3+6xyz

Question

因式分解x^3-y^3+8z^3+6xyz
阅读：
a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-ac-bc)
根据上面提示分解因式
x^3-y^3+8z^3+6xyz

Answer 1

x^3-y^3+8z^3+6xyz
=x^3+(-y)^3+(2z)^3-3x(-y)(2z)
=[x+(-y)+2z][x^2+(-y)^2+(2z)^2-x(-y)-x(2z)-(-y)(2z)]
=(x-y+2z)(x^2+y^2+4z^2+xy-2xz+2yz)