verify x3+ y3+ z3- 3xyz=(x+y+z) [(x-y)2+ (y-z)2 +( z-x)2)] - Maths - Polynomials

Question

verify x3+ y3+ z3- 3xyz=(x+y+z) [(x-y)2+ (y-z)2 +( z-x)2)]

Rishabh Mittal · Accepted Answer

To verifyx3+y3+z3-3 xyz=x+y+zx-y2+y-z2+z-x2LHSx3+y3+z3-3 xyz=x+y+zx2+y2+z2-xy-yz-zxRHSx+y+zx-y2+y-z2+z-x2=x+y+zx2-2xy+y2+y2-2yz+z2+z2-2zx+x2=x+y+z2x2+y2+z2-xy-yz-zx=2x+y+zx2+y2+z2-xy-yz-zxSo, LHS≠RHS