Answer
$a^{3}$ - 18$a^{2}$ + 108a - 216
Work Step by Step
$(a-6)^{3}$ = (a-6)(a-6)(a-6) =
(a-6)(a-6) $\times$ (a-6) =
($a^{2}$ - 2$\times$a$\times$6 + $6^{2}$) $\times$ (a-6) =
($a^{2}$ - 12a + 36) $\times$ (a - 6) =
RECALL:
The distributive property states that for any real numbers a, b, and c:
a(b+c)=ab+ac
a(b−c)=ab−ac
Use the distributive property (which is shown above) to obtain:
a($a^{2}$ - 12a + 36) - 6($a^{2}$ - 12a + 36) =
$a^{3}$ - 12$a^{2}$ + 36a - 6$a^{2}$ + 72a - 216 =
Simplify.
$a^{3}$ - 18$a^{2}$ + 108a - 216
