\(x^4+4y^4\)
\(= (x^2)^2 + 4x^2y^2 + (2y^2)^2 - 4x^2y^2\)
\(= (x^2+2y^2)^2-(2xy)^2\)
\(=(x^2+2xy+2y^2)(x^2-2xy+2y^2)\)
\(x^4+y^4\)
\(=(x^2)^2 + 2x^2y^2+(y^2)^2 - 2x^2y^2\)
\(=\left(x^2+y^2\right)^2-\left(\sqrt{2}xy\right)^2\)
\(=\left(x^2+\sqrt{2}xy+y^2\right)\left(x^2-\sqrt{2}xy+y^2\right)\)
\(x^4+324 \)
\(=\left(x^2\right)^2+36x^2+18^2-36x^2\)
\(=\left(x^2+18\right)^2-\left(6x\right)^2\)
\(=\left(x^2+6x+18\right)\left(x^2-6x+18\right)\)
\(4x^4+y^4\)
\(=\left(2x^2\right)^2+4x^2y^2+\left(y^2\right)^2-4x^2y^2\)
\(=\left(2x^2+y^2\right)^2-\left(2xy\right)^2\)
\(=\left(2x^2+2xy+y^2\right)\left(2x^2-2xy+y^2\right)\)
