\(4x^4+1=4x^4+4x^2+1-4x^2\)
\(=\left(2x^2\right)^2+2.2x^2+1^2-\left(2x\right)^2\)
\(=\left(2x^2+1\right)^2-\left(2x\right)^2\)
\(=\left[\left(2x^2+1\right)-2x\right].\left[\left(2x^2+1\right)+2x\right]\)
\(=\left(2x^2+1-2x\right).\left(2x^2+1+2x\right)\)
\(=\left(2x^2-2x+1\right).\left(2x^2+2x-1\right)\)
\(=\left(2x^2-2x+1\right).\left(2x^2+2x-1\right)\)
4x4+4x2+1-4x2=(2x2+1)2-(2x)2=(2x2+1-2x)(2x2+1-2x)