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\left(7x^{3}-11y^{2}\right)\left(7x^{3}+11y^{2}\right)
Rewrite 49x^{6}-121y^{4} as \left(7x^{3}\right)^{2}-\left(11y^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).