Question

x^8-256 please solve it

Answer 1

$\textbf{ Hello Mate! }$

${x}^{8} - 256 \\ = {x}^{8} - {2}^{8} \\ = { ({x}^{4} )}^{2} - { ({2}^{4}) }^{2} \\ {a}^{2} - {b}^{2} = (a + b)(a - b) \\ = ( {x}^{4} + {2}^{4} )( {x}^{4} - {2}^{4} ) \\ = ( {x}^{4} + {2}^{4} )( { ({x}^{2}) }^{2} - { ({2}^{2}) }^{2} ) \\ = ( {x}^{4} + {2}^{4} )( {x}^{2} + {2}^{2} )( {x}^{2} - {2}^{2} ) \\ = ( {x}^{4} + 16 )( {x}^{2} + 4)(x + 2)(x - 2)$

Have great future ahead!

Answer 2

x8−256=x8−28=(x4)2−(24)2a2−b2=(a+b)(a−b)=(x4+24)(x4−24)=(x4+24)((x2)2−(22)2)=(x4+24)(x2+22)(x2−y2)=(x4+16)(x2+4)(x+y)(x−y)​