Question

Factorise

x^4-(x-z)^4

Answer 1

★ Question :

Factorise

$x {}^{4} - (x - z) {}^{4}$

★ Answer :

$x {}^{4} - (x - z) {}^{4}$

$= (x {}^{2} ) {}^{2} - ((x - z) {}^{2} ) {}^{2}$

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

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

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

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Answer 2

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