\(81x^4+4y^4=\left(81x^4+36x^2y^2+4y^4\right)-36x^2y^2\)
\(=\left(9x^2+2y^2\right)^2-36x^2y^2\)
\(=\left(9x^2+2y^2-6xy\right)\left(9x^2+2y^2+6xy\right)\)
\(81x^4+4y^4=81x^4+36x^2y^2+4y^4-36x^2y^2=\left(9x^2+2y^2\right)^2-\left(6xy\right)^2=\left(9x^2+2y^2-6xy\right)\left(9x^2+2y^2+6xy\right)\)