Question

1-x16 розклади на множники

Answer 1

$1-x^{16}=1^{2} -(x^{8} )^{2} =(1-x^{8} )(1+x^{8} )=[1^{2} -(x^{4})^{2}](1+x^{8} )=\\\\=(1-x^{4})(1+x^{4})(1+x^{8})=[(1^{2} -(x^{2} )^{2}](1+x^{4} )(1+x^{8})=\\\\=(1-x^{2})(1+x^{2})(1+x^{4})(1+x^{8})=\boxed{(1-x)(1+x)(1+x^{2})(1+x^{4})(1+x^{8})}$