Question

Factorise xpower 12 -4power12

Answer 1

${x}^{12} - {4}^{12} \\ = { ({x}^{6})}^{2} - { ({4}^{6})}^{2} \\ = ( {x}^{6} - {4}^{6})( {x}^{6} + {4}^{6}) \\ = ({ ({x}^{3} )}^{2} - { ({4}^{3} )}^{2})( {x}^{6} + 4096) \\ = ( {x}^{3} - {4}^{3} )( {x}^{3} + {4}^{3} )( {x}^{6} + 4096) \\ = (x - 4)( {x}^{2} + {4}^{2} + 4x)(x + 4)( {x}^{2} + {4}^{2} - 4x)( {x}^{6} + 4096) \\ = (x - 4)( {x}^{2} + 16 + 4x)(x + 4)( {x}^{2} + 16 - 4x)( {x}^{6} + 4096)$