Elementary Algebra

$x^{3}$ - 9$x^{2}$ + 27x - 27
$(x - 3)^{3}$ = (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