Question

verify x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]​

Answer 1

Step-by-step explanation:

From R.H.S = 1/2(x+y+z) [( x- y)^2 (y-z)^2 (z-x)^2]. =1/2(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]. =1/2(x+y+z)2[x^2+y^2+z^2-xy-yz-zx]. =(x+y+z)[x^2+y^2+z^2-xy-yz-zx]. =x^3+xy^2+xz^2-x^2y-xyz-x^2z+x^2y+y^3+yz^2-xy^2-y^2z-xyz+x^2z+y^2z+z^3-xyz-yz^2-xz^2. =x^3+y^3+z^3-3xyz.