Answer
$a^{3}$ + 15$a^{2}$ + 75a + 125
Work Step by Step
$(a + 5)^{3}$ = (a + 5) $\times$ (a + 5) $\times$ (a + 5) =
(a + 5)(a + 5) $\times$ (a + 5) =
($a^{2}$ + 2$\times$a$\times$5 + $5^{2}$) $\times$ (a + 5) =
($a^{2}$ + 10a + 25) $\times$ (a + 5) =
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($a^{2}$ + 10a + 25) + 5($a^{2}$ + 10a + 25) =
$a^{3}$ + 10$a^{2}$ + 25a + 5$a^{2}$ + 50a + 125 =
Simplify.
$a^{3}$ + 15$a^{2}$ + 75a + 125
