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\left(2x-9y^{2}\right)\left(2x+9y^{2}\right)
Rewrite 4x^{2}-81y^{4} as \left(2x\right)^{2}-\left(9y^{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).