Question

If $x+y+z=0$, then $x^3+y^3+z^3$ = ..........

• A. $3xyz$
• B. $x^{2}yz$
• C. $x{y}^{2}z$
• D. $xy{z}^2$

Answer 1

The correct option is A $3xyz$

$x+y+z=0\Rightarrow x+y=-z$
Cubing on both sides,
$(x+y{)}^3=(-z{)}^3$
$\Rightarrow x^3+y^3+3xy(x+y)=z^3$
$\Rightarrow x^3+y^3+3xy(-z)=-z^3$
$\Rightarrow x^3+y^3-3xyz+z^3=0$
$\therefore x^3+y^3+z^3=3xyz$