Question

a-2b+3c=0 find a^3-8b^3+27c^3

Answer 1

$\huge\purple{\bf{ANSWER}}$

$\rm{a - 2b + 3c = 0}$

$\rm{or \: a - 2b = - 3c}$

$\rm{now \: cubing \: on \: both \: sides}$

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

$\rm{use \: formula \: \rightarrow{(a - b)}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b)}$

$\rm{ {a}^{3} - {(2b)}^{3} - 3(a)(2b)(a - 2b) = { - 27c}^{3} }$

$\rm{ {a}^{3} - {8b}^{3} - 6ab( - 3c) } = - 27{c}^{3}$

$\rm{ {a}^{3} - {8b}^{3} - 18abc} = - 27{c}^{3}$

$\fbox{\rm{ {a}^{3} - {8b}^{3} + 27{c}^{3} = 18abc}}$