$x^{8}$$y^{8}$ + $x^{4}$$y^{4}$ +1
= $x^{8}$$y^{8}$ + 2$x^{4}$$y^{4}$ +1 - $x^{4}$$y^{4}$
= ( $x^{4}$$y^{4}$ +1 ) - $x^{4}$$y^{4}$
= ( $x^{4}$$y^{4}$ +1 ) -$(x^{2}$$y^{2})^{2}$
= ( $x^{4}$$y^{4}$ +1 - $x^{2}$$y^{2}$ ) . ( $x^{4}$$y^{4}$ +1 + $x^{2}$$y^{2}$ )