Question

verify that x3+y3+z3-3xyz=1/2(x+y+z){(x-y)^2+(y-z)^2+(z-x)^2}

Answer 1

$\huge \boxed{ \mathbb{ \ulcorner ANSWER: \urcorner}}$




$\boxed{See \: the \: attachment \: for \: your \: answer.}$


✔✔ Hence, it is verified ✅✅.

____________________________________




$\huge \boxed{ \mathbb{THANKS}}$



$\huge \bf{ \# \mathbb{B}e \mathbb{B}rainly.}$

Answer 2

here is your answer OK

x3 + y3+z3-3xyz = (x + y + z) (x2 + y2 + z2- xy -yz -zx)

=1/2 (2x2 + 2y2 + 2z2 - 2zy - 2yz- 2zx)
= 1/2 (x + y + z){(x2- 2yx + y2) (y2 -2yz + z2) (z2 -2zx +x2)}
​= 1/2 (x+y+z) [(x-y)2 + (y-z)2 + (z-x)2]