Question

因式分解：（x+y+z)^5-x^5-y^5-z^5.

Answer 1

因式分解=[（x+y+z)^5-x^5]-(y^5+z^5)

=（x+y+z-x）[(x+y+z)^4+x(x+y+z)^3+

x^2(x+y+z)^2+x^3(x+y+z)+x^4]-

(y+z)(y^4-y^3z+y^2z^2-yz^3+z^4)

=(y+z)[(x+y+z)^4+x(x+y+z)^3+x^2(x+y+z)^2+

x^3(x+y+z)+x^4-y^4+y^3z-y^2z^2+yz^3-z^4]