Question

已知x+y+z=0,则x3+x2z+y2z-xyz+y3的值为? 要有具体的解题过程!

Answer 1

x3+x2z+y2z-xyz+y3=x^3+x^2z+x^2y-x^2y+y^2z-xyz+y^3+y^2x-y^2x =x^2(x+z+y)+(y^3+y^2z+y^2x)-(x^2y+xy^2+xyz) =x^2(x+y+z)+y^2(x+y+z)-xy(x+y+z) =(x^2+y^2-xy)(x+y+z) =0