# How do you factor the difference of two cubes x^3 - 216?

Apr 9, 2015

Remember this formula for factorizing difference of 2 cubes:
a^3−b^3=(a−b)(a^2+ab+b^2)

In ${x}^{3} - 216$,

${a}^{3} = {x}^{3}$
${b}^{3} = 216$

$a = \sqrt[3]{{x}^{3}}$ = $x$
$b = \sqrt[3]{216}$= $6$

Substitute $a = x$ , $b = 6$ into the formula of $\left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$

$\left(x - 6\right)$(x^2 + ($6$x$x$) + ${6}^{2}$) = $\left(x - 6\right)$(x^2 + $6 x$+ 36)

$\left(x - 6\right)$(x^2 + $6 x$+ 36) is the factorized form of ${x}^{3} - 216$