Question

If $a,b,c$ are in A.P prove that:
$a^3+c^3+6abc=8b^3$

Answer 1

$8b^3=8{\left(\frac{a+c}{2}\right)}^3$

$=(a+c{)}^3$

$=a^3+c^3+3ac(a+c)$

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

$=a^3+c^3+6abc$