Answer
This statement is true.
Work Step by Step
($x^{2}$ - x - 1)($x^{2}$ + x + 1) = $x^{4}$ - $x^{2}$ - 2x - 1
We simplify the left side.
Use the distributive property to expand the left side.
($x^{2}$ - x - 1)($x^{2}$ + x + 1) =
($x^{2}$$\times$$x^{2}$ + $x^{2}$$\times$x + $x^{2}$$\times$1) - (x$\times$$x^{2}$ + x$\times$x + x$\times$1) - ($x^{2}$ + x + 1) =
($x^{4}$ + $x^{3}$ + $x^{2}$) - ($x^{3}$ + $x^{2}$ + x) - ($x^{2}$ + x + 1) =
Remove parentheses.
$x^{4}$ + $x^{3}$ + $x^{2}$ - $x^{3}$ - $x^{2}$ - x - $x^{2}$ - x - 1 =
Simplify.
$x^{4}$ - $x^{2}$ - 2x - 1
Because $x^{4}$ - $x^{2}$ - 2x - 1 is equal to $x^{4}$ - $x^{2}$ - 2x - 1, this statement is true.
