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\left(9x^{2}-4\right)\left(9x^{2}+4\right)
Rewrite 81x^{4}-16 as \left(9x^{2}\right)^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(3x-2\right)\left(3x+2\right)
Consider 9x^{2}-4. Rewrite 9x^{2}-4 as \left(3x\right)^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(3x-2\right)\left(3x+2\right)\left(9x^{2}+4\right)
Rewrite the complete factored expression. Polynomial 9x^{2}+4 is not factored since it does not have any rational roots.