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\left(13a-14b\right)\left(13a+14b\right)
Rewrite 169a^{2}-196b^{2} as \left(13a\right)^{2}-\left(14b\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).