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