Question

If x+y+2=0 then $x^3+y^3+8$ is ...........

• A. ${(x+y+z)}^2$
• B. 0
• C. 6 xy
• D. -6 xy

Answer 1

The correct option is D -6 xy

$x+y+2=0$

$\Rightarrow x+y=-2$

$\Rightarrow {(x+y)}^3={(-2)}^3$ by cubing both sides

$\Rightarrow x^3+y^3-3xy(x+y)=-8$

$\Rightarrow x^3+y^3-3xy(-2)=-8$ since $x+y=-2$

$\Rightarrow x^3+y^3+8+6xy=0$

$\therefore x^3+y^3+8=-6xy$