Question

28. (Factorise): x4 - (x – z)4​

Answer 1

Answer:

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

Step-by-step explanation:

$x ^{4} - (x - z {)}^{4} \\ = )since \: a^{2} - {b }^{2} = (a + b)(a - b) \\ = )( {x}^{2} - (x - z {)}^{2})( {x}^{2} + (x + z {)}^{2} ) \\ = )(x - (x - z)(x + (x - z))( {x}^{2} + {x}^{2} - 2xz + {z}^{2} ) \\ = )(x - x + z)(x + x - z)( {2x}^{2} - 2xz + {z}^{2} ) \\ = )(z)(2x - z)(2x^{2} - 2xz + {z}^{2} )$