Answer
$x^{3}$ - 3$x^{2}$ + 3x - 1
Work Step by Step
$(x - 1)^{3}$ =
(x - 1)(x - 1)(x - 1) =
Remember that $(a-b)^{2}$ = $a^{2}$ - 2ab + $b^{2}$
So, (x - 1)(x - 1)(x - 1) =
($x^{2}$ - 2$\times$x$\times$1 + $1^{2}$)(x - 1) =
($x^{2}$ - 2x + 1)(x - 1) =
Use the distributive property.
$x^{2}$(x) +$x^{2}$(-1) -2x(x) -2x(-1) +1(x) +1(-1) =
$x^{3}$ - $x^{2}$ - 2$x^{2}$ + 2x + x - 1 =
Simplify.
$x^{3}$ - 3$x^{2}$ + 3x - 1
