Question:
Factorize each of the following algebraic expression:
4x4 + 1
Solution:
$4 x^{4}+1$
$=4 \mathrm{x}^{4}+4 \mathrm{x}^{2}+1-4 \mathrm{x}^{2}$
$=\left[\left(2 \mathrm{x}^{2}\right)^{2}+2 \times 2 \mathrm{x}^{2} \times 1+1\right]-4 \mathrm{x}^{2}$
$=\left(2 \mathrm{x}^{2}+1\right)^{2}-(2 \mathrm{x})^{2}$
$=\left[\left(2 \mathrm{x}^{2}+1\right)-2 \mathrm{x}\right]\left[\left(2 \mathrm{x}^{2}+1\right)+2 \mathrm{x}\right]$
$=\left(2 \mathrm{x}^{2}-2 \mathrm{x}+1\right)\left(2 \mathrm{x}^{2}+2 \mathrm{x}+1\right)$
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