Question

factorise this-
x⁸-y⁸​

Answer 1

(x-y) to the power 8 is the answer mate.

Answer 2

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

Explanation:-

We know that

${x}^{2} - {y}^{2} = (x + y)(x - y)$

so

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