## Elementary Algebra

$a^{3}$ + 15$a^{2}$ + 75a + 125
$(a + 5)^{3}$ = (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