Question

Factor a^4-16b^8 using only real factors

Answer 1

`\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ a^4 - 16b^8\implies (a^2)^2-2^4 b^8\implies (a^2)^2-(2^2)^2 (b^4)^2\implies \underset{\textit{diff. of squares}}{(a^2)^2 - (2^2 b^4)^2} \\\\\\\ [a^2-2^2 b^4][a^2+2^2 b^4]\implies [a^2-2^2 (b^2)^2][a^2+2^2 b^4] \\\\\\\ \underset{\textit{diff. of squares}}{[a^2-(2 b^2)^2]}[a^2+4 b^4] \implies {\Large \begin{array}{llll} (a-2b^2)(a+2b^2) ~~ (a^2+4b^4) \end{array}}`