Question

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

• A. $-2abc$
• B. $-6abc$
• C. $6abc$
• D. $2abc$

Answer 1

The correct option is B $-6abc$

Given : $a,b,c$ are in A.P., so
$2b=a+c$
Now,
$a^3+c^3-8b^3=a^3+c^3-(2b{)}^3=a^3+c^3-(a+c{)}^3=a^3+c^3-(a^3+c^3+3ac(a+c\left)\right)=-3ac\left(2b\right)=-6abc$