Question

a^8-b^8
a^4-b^4
a^4-a^3+a-1

Answer 1

$a^8-b^8 = ( {a}^{4} - {b}^{4} ) ( {a}^{4} + {b}^{4} ) \\ a^4-b^4 = ( {a}^{2} - {b}^{2} ) ( {a}^{2} + {b}^{2} ) \\ a^4-a^3+a-1 = {a}^{3} (a - 1) + (a -1 ) = \\ = (a - 1)( {a}^{3} - 1)$