expand-1-x-8-

Question Number 132682 by otchereabdullai@gmail.com last updated on 15/Feb/21

expand 1 - x^{8}

Answered by MJS_new last updated on 15/Feb/21

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

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

Commented by otchereabdullai@gmail.com last updated on 15/Feb/21

God bless u prof mjs

Answered by mathmax by abdo last updated on 16/Feb/21

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

= (1 - x) (1 + x) (1 + x^{2}) ({(1 + x^{2})}^{2} - {2 x}^{2})

= (1 - x) (1 + x) (1 + x^{2}) (x^{2} - \sqrt{2} x + 1) (x^{2} + \sqrt{2} x + 1)