Question

If $a+b+2c=0,$ then the value of $a^3+b^3+8c^3$ is equal to:

• A. $3abc$
• B. $4abc$
• C. $abc$
• D. $6abc$

Answer 1

The correct option is D $6abc$

We know,

$x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)$.

When $x+y+z=0$,

then $x^3+y^3+z^3-3xyz=\left(0\right)(x^2+y^2+z^2-xy-yz-zx)$

$⟹$ $x^3+y^3+z^3-3xyz=0$

$⟹$$x^3+y^3+z^3=3xyz$.

Similarly, if $a+b+2c=0$,

then $a^3+b^3+8c^3=3\times \left(a\right)\left(b\right)\left(2c\right)=6abc$.

Therefore, option $D$ is correct.