\(x^4-4y^4\)
\(=\left(x^2\right)^2-\left(2y^2\right)^2\)
\(=\left(x^2-2y^2\right)\left(x^2+2y^2\right)\)
\(x^4-4y^4\)
\(=\left(x^2\right)^2-\left(2y\right)^2\)
\(=\left(x^2-2y\right)\left(x^2+2y\right)\)
\(x^4+4y^4\)
\(=\left(x^2\right)^2+\left(2y^2\right)^2\)
\(=\left(x^2+y^2\right)^2-\left(2xy\right)^2\)
\(=\left(x^2+2y^2-2xy\right)\left(x^2+2y^2+2xy\right)\)