facorise:x^3(y-z)^3+ y^3(z-x)^3+ z^3(x-y)^3 Share with your friends Share 0 Ashwini Kumar answered this We have,x3y-z3+y3z-x3+z3x-y3=xy-z3+yz-x3+zx-y3=xy-zx3+yz-xy3+zx-yz3We know that when a+b+c=0, thena3+b3+c3=3abcHere,xy-zx+yz-xy+zx-yz=0∴xy-zx3+yz-xy3+zx-yz3=3xy-zxyz-xyzx-yzHence, x3y-z3+y3z-x3+z3x-y3=3xy-zxyz-xyzx-yz=3xy-z×yz-x×zx-y=3xyzy-zz-xx-y 0 View Full Answer Swagat Swargari answered this x3(y - z)3 + y3(z - x)3 + z3(x - y)3 can be written as {x(y - z)}3 + {y(z - x)}3 + {z(x - y)}3 using identity: a3 + b3 + c3- 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca) if a + b + c = 0; then a3 + b3 + c3- 3abc = 0 or a3 + b3 + c3= 3abc Here, {x(y - z)} + {y(z - x)} + {z(x - y)} = xy - xz + yz - xy + xz - yz = 0 so, {x(y - z)}3 + {y(z - x)}3 + {z(x - y)}3 = 3*{x(y - z)}*{y(z - x)}*{z(x - y)} = 3xyz(y - z)(z - x)(x - y) 0
