Question

Factorise - y {}^{8} " alt="x {}^{8} - y {}^{8} " align="absmiddle" class="latex-formula">

Answer 1

Solution :
$x {}^{8} - y {}^{8} = (x {}^{4} ) {}^{2} - (y {}^{4} ) {}^{2}$
$= (x {}^{4} + y {}^{4} )(x {}^{4} - y {}^{4} )$
$= (x {}^{4} + y {}^{4} )[(x {}^{2} ) {}^{2} - (y {}^{2} )]$
$= (x {}^{4} + y {}^{4} )(x {}^{2} + y {}^{2} )(x {}^{2} - y {}^{2} )$
$= (x {}^{4} + y {}^{4} )(x {}^{2} + y {}^{2} )(x + y)(x - y)$