Answer
$n^{4}$ - 5$n^{3}$ - 11$n^{2}$ - 30n - 4
Work Step by Step
($n^{2}$ + 2n + 4)($n^{2}$ - 7n - 1) =
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:
$n^{2}$($n^{2}$ - 7n - 1) + 2n($n^{2}$ - 7n - 1) + 4($n^{2}$ - 7n - 1) =
$n^{4}$ - 7$n^{3}$ - $n^{2}$ + 2$n^{3}$ - 14$n^{2}$ - 2n + 4$n^{2}$ - 28n - 4 =
Group similar terms.
$n^{4}$ + (-7$n^{3}$ + 2$n^{3}$) + (-$n^{2}$ - 14$n^{2}$ + 4$n^{2}$) + (-2n - 28n) - 4 =
Simplify.
$n^{4}$ - 5$n^{3}$ - 11$n^{2}$ - 30n - 4
