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4\left(4a^{8}-b^{2}\right)
Factor out 4.
\left(2a^{4}-b\right)\left(2a^{4}+b\right)
Consider 4a^{8}-b^{2}. Rewrite 4a^{8}-b^{2} as \left(2a^{4}\right)^{2}-b^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).
4\left(2a^{4}-b\right)\left(2a^{4}+b\right)
Rewrite the complete factored expression.