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