Question

If a,b,c are in A.P., then $a^3+c^3-{8b}^3$ is equal to

• A. $2abc$
• B. $6abc$
• C. $4abc$
• D. none of these

Answer 1

The correct option is D none of these

As $a,b,c$ are in A.P

$2b=a+c$

$\Rightarrow 8b^3=(a+c{)}^3=a^3+c^3+3ac(a+c)$

$\Rightarrow 8b^3=a^3+c^3+3ac\left(2b\right)$

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