## Elementary Algebra

($x^{2}$ - 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}$$\timesx + x^{2}$$\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.