Question

how to factor x^8-1

Answer 1

\(\bf x^8-1\\ \quad \\
\textit{keep in mind that}\quad 1^8 \implies 1\qquad thus\\ \quad \\
x^8-1\implies x^8-1^8\implies (x^4)^2-(1^4)^2\implies [(x^2)^2]^2-[(1^2)^2]^2\\ \quad \\
\textit{recall that }\qquad a^2-b^2 = (a-b)(a+b)\)