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a^{4}\left(27b^{3}+64a^{3}\right)
Factor out a^{4}.
\left(4a+3b\right)\left(16a^{2}-12ab+9b^{2}\right)
Consider 27b^{3}+64a^{3}. Rewrite 27b^{3}+64a^{3} as \left(4a\right)^{3}+\left(3b\right)^{3}. The sum of cubes can be factored using the rule: p^{3}+q^{3}=\left(p+q\right)\left(p^{2}-pq+q^{2}\right).
a^{4}\left(4a+3b\right)\left(16a^{2}-12ab+9b^{2}\right)
Rewrite the complete factored expression.