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\left(6s-11t\right)\left(6s+11t\right)
Rewrite 36s^{2}-121t^{2} as \left(6s\right)^{2}-\left(11t\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).