## Elementary Algebra

$x^{4}$ + $x^{3}$ + 2$x^{2}$ - 7x - 5
($x^{2}$ - 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