Question

Factorise this : x^8 - y^8

Answer 1

x^8 - y^8

=> (x^4)^2 - (y^4)^2

=> ( x^4 - y^4) (x^4 + y^4)

=> [ (x^2)^2 - (y^2)^2] (x^4 + y^4)

=> (x^2 - y^2) ( x^2 +y^2) (x^4 + y^4)

=> (x-y) (x+y) (x^2 +y^2) (x^4 + y^4)

Answer 2

$Hi \: \: !!! \\ \\ Here \: \: is \: \: your \: \: answer, \\ \\ Factorise \: \: \: {x}^{8} - {y}^{8} \\ \\ {( {x}^{4} )}^{2} - {( {y}^{4} )}^{2} \\ \\ ( {x}^{4} + {y}^{4} )( {x}^{4} - {y}^{4} ) \\ \\ ( {x}^{4} + {y}^{4} )( {( {x}^{2} )}^{2} - { ({y}^{2} )}^{2} ) \\ \\ ( {x}^{4} + {y}^{4} )( {x}^{2} + {y}^{2} )( {x}^{2} - {y}^{2} ) \\ \\ ( {x}^{4} + {y}^{4} )( {x}^{2} + {y}^{2} )( {( {x}^{2}) }^{2} - {(y)}^{2} ) \\ \\ ( {x}^{4} + {y}^{4} )( {x}^{2} + {y}^{2} )( x- y )(x - y) \\ \\ \\ Hope \: \: it \: \: helps.$