Question

Verify that x³+y³+z³-3xyz=½( x+y+z )((x-y)²+(y-z)²+(z-x)²) ?​

Answer 1

Answer:

x^3+y^3+z^3-3xyz=

1/2(x+y+z)((xy)^2+(y-z)^2+(z-x)^2)

using identity (a-b)^2=a^2+b^2+2ab

(X+y+z)(x^2+y^2-2xy+y^2+z^2-2yz+z^2+x^2-2zx)

1/2(X+y+z)(2x^2+2y^2+2z^2-2xy-2yz-2zx)

make 2common

1/2*2(X+y+z)(x^2+y^2+z^2-xy-yz-zx)

verify LHS =RHS

I think you are in 9 th class please follow me