Answer
$x^{3}$ - 9$x^{2}$ + 27x - 27
Work Step by Step
$(x - 3)^{3}$ =
(x - 3)(x - 3)(x - 3) =
Remember that $(a-b)^{2}$ = $a^{2}$ - 2ab + $b^{2}$.
So, (x - 3)(x - 3)(x - 3) =
($x^{2}$ - 2$\times$x$\times$3 + $3^{2}$)(x - 3) =
($x^{2}$ - 6x + 9)(x - 3) =
Use the distributive property.
$x^{2}$(x) +$x^{2}$(-3) -6x(x) -6x(-3) +9(x) +9(-3) =
$x^{3}$ - 3$x^{2}$ - 6$x^{2}$ + 18x + 9x - 27 =
Simplify.
$x^{3}$ - 9$x^{2}$ + 27x - 27