Question

If a + 2b + c = 0; then evaluate $a^3+8b^3+c^3$

• A. 3abc
• B. 6abc
• C. abc
• D. 0.0

Answer 1

The correct option is B 6abc

Given that a+2b+c=0;
$\therefore a+2b=-c$ ...... (1)

Cubing both sides of the above equation,

$(a+2b{)}^3=(-c{)}^3$

$a^3+8b^3+3\times a\times 2b(a+2b)=(-c{)}^3$ $[\because (a+b{)}^3=a^3+b^3+3ab(a+b)]$

$a^3+8b^3+3\times a\times 2b(-c)=(-c{)}^3$ ....... [ from (1)]

$a^3+8b^3-6abc=(-c{)}^3$

$\therefore a^3+8b^3+c^3=6abc$

Hence the correct answer is option (B).