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factorise :- x^8-y^8

x8 - y8

= (x4)2 - (y4)2

= (x4 - y4) (x4 + y4)

= (x2)2 - (y2)2  (x4 + y4)

= (x2 - y2) (x2 + y2) (x4 + y4)

= (x -y) (x + y) (x2 + y2) (x4 + y4)  Ans

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Tjis uses the identity ----   a3 - b3  = ( a - b ) ( a2 - ab -b2 )
                                                             

x8 -y8 = ( x2 -y2 ) ( x4 - x2y2 -y4 )      [ To understand this better we will take a as x2 because x2's cube is x8 and    .                                                                b    as y8 because y2's cube is y8 ] 

HOPE THIS HELPS

           
         

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