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\left(3a-8b\right)\left(3a+8b\right)
Rewrite 9a^{2}-64b^{2} as \left(3a\right)^{2}-\left(8b\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).