Question
Solve:
$4 x^4+1$
$4 x^4+1$
✓
Answer
$4 x^4+1$
$=4 x^4+4 x^2+1-4 x^2$
$=\left[(2 x)^2+2 \times 2 x^2 \times 1+1\right]-4 x^2$
$=\left(2 x^2+1\right)-(2 x)^2$
$=\left[\left(2 x^2+1\right)-2 x\right]\left[\left(2 x^2+1\right)+2 x\right]$
$=\left(2 x^2-2 x+1\right)\left(2 x^2+2 x+1\right)$
$=4 x^4+4 x^2+1-4 x^2$
$=\left[(2 x)^2+2 \times 2 x^2 \times 1+1\right]-4 x^2$
$=\left(2 x^2+1\right)-(2 x)^2$
$=\left[\left(2 x^2+1\right)-2 x\right]\left[\left(2 x^2+1\right)+2 x\right]$
$=\left(2 x^2-2 x+1\right)\left(2 x^2+2 x+1\right)$
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