Question

Factorise: (x⁸-1)
Please Factorise this in Short Form​

Answer 1

Step-by-step explanation:

${x}^{8} - 1 = ( {x}^{4}) ^{2} - 1)^{2} \\ = ({x}^{4} - 1)( {x}^{4} + 1) \\ =( ( {x}^{2}) ^{2} - 1^{2} )( {x}^{4} + 1) \\ = ( {x}^{2} - 1)( {x}^{2}+ 1)( {x}^{4} + 1) \\ = ((x)^{2} - {1}^{2} )( {x}^{2} + 1)( {x}^{4} + 1) \\ = (x - 1)(x + 1)( {x}^{2} + 1)( {x}^{4} + 1)$