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\left(a+2b-8\right)\left(a+2b+8\right)
Rewrite a^{2}+4b^{2}+4ab-64 as \left(a+2b\right)^{2}-8^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).