How do you factor the difference of two cubes $x^{3} - 216$ $x^3 - 216$ ?

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Answer 1 · 2015-04-09T04:07:24

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

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

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

$a = \sqrt[3]{x^{3}}$ $a= root3(x^3)$ = $x$ $x$
$b = \sqrt[3]{216}$ $b=root3(216)$ = $6$ $6$

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

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

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

How do you factor the difference of two cubes x^3 - 216x3−216x^3 - 216?