\(4x^4+1\)
\(=4x^4+4x^2+1-4x^2\)
\(=\left(4x^4+4x^2+1\right)-4x^2\)
\(=\left(2x^2+1\right)^2-4x^2\)
\(=\left(2x^2-2x+1\right)\left(2x^2+2x+1\right)\)
\(16x^4+4\)
\(=4\left(4x^4+1\right)\)
\(=4\left(4x^4+4x^2+1-4x^2\right)\)
\(=4\left[\left(4x^4+4x^2+1\right)-\left(2x\right)^2\right]\)
\(=4\left[\left(2x^2+1\right)^2-\left(2x\right)^2\right]\)
\(=4\left(2x^2+1-2x\right)\left(2x^2+1+2x\right)\)
f) $4x^4+1$
$=(4x^4+4x^2+1)-4x^2$
$=[(2x^2)^2+2\cdot2x^2\cdot1+1^2]-(2x)^2$
$=(2x^2+1)^2-(2x)^2$
$=(2x^2+1-2x)(2x^2+1+2x)$
g) $16x^4+4$
$=(16x^4+16x^2+4)-16x^2$
$=[(4x^2)^2+2\cdot4x^2\cdot2+2^2]-(4x)^2$
$=(4x^2+2)^2-(4x)^2$
$=(4x^2+2-4x)(4x^2+2+4x)$
$=[2(2x^2-2x+1)][2(2x^2+2x+1)]$
$=4(2x^2-2x+1)(2x^2+2x+1)$