Question

24. xy⁹-yx⁹
tell fast factorize this ​

Answer 1

Answer:

$x {y}^{9} - y {x}^{9}$

$xy( {y}^{8} - {x}^{8} )$

$xy( { ({y}^{4}) }^{2} - {( {x}^{4} )}^{2} )$

$xy( {y}^{4} + {x}^{4} )( {y}^{4} - {x}^{4} )$

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

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

Answer 2

$: \implies x {y}^{9} - y {x}^{9} \\ \\: \implies xy \times {y}^{8} - xy \times {x}^{8} \\ \\ : \implies xy( {y}^{8} - {x}^{8} ) \\ \\ : \implies xy( {y}^{4} + {x}^{4} )( {y}^{4} - {x}^{4} ) \\ \\ : \implies xy( {y}^{4} + {x}^{4} )( {y}^{2} + {x}^{2} )( {y}^{2} - {x}^{2} ) \\ \\ : \implies (xy)( {y}^{4} + {x}^{4} )( {y}^{2} + {x}^{2} )( {y} + x)(y - x)$

Hope it's helpful to you