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\left(8-5c\right)\left(8+5c\right)
Rewrite 64-25c^{2} as 8^{2}-\left(5c\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(-5c+8\right)\left(5c+8\right)
Reorder the terms.