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\left(8a^{3}b-7c^{4}\right)\left(8a^{3}b+7c^{4}\right)
Rewrite 64a^{6}b^{2}-49c^{8} as \left(8a^{3}b\right)^{2}-\left(7c^{4}\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).
\left(8ba^{3}-7c^{4}\right)\left(8ba^{3}+7c^{4}\right)
Reorder the terms.