Factorize each of the following algebraic expression:
4x4 + y4
$4 x^{4}+y^{4}$
$=4 \mathrm{x}^{4}+4 \mathrm{x}^{2} \mathrm{y}^{2}+\mathrm{y}^{4}-4 \mathrm{x}^{2} \mathrm{y}^{2}$
$=\left[\left(2 \mathrm{x}^{2}\right)^{2}+2 \times 2 \mathrm{x}^{2} \times \mathrm{y}+\left(\mathrm{y}^{2}\right)^{2}\right]-(2 \mathrm{xy})^{2}$
$=\left(2 \mathrm{x}^{2}+\mathrm{y}^{2}\right)^{2}-(2 \mathrm{xy})^{2}$
$=\left[\left(2 \mathrm{x}^{2}+\mathrm{y}^{2}\right)-2 \mathrm{xy}\right]\left[\left(2 \mathrm{x}^{2}+\mathrm{y}^{2}\right)+2 \mathrm{xy}\right]$
$=\left(2 \mathrm{x}^{2}-2 \mathrm{xy}+\mathrm{y}^{2}\right)\left(2 \mathrm{x}^{2}+2 \mathrm{xy}+\mathrm{y}^{2}\right)$
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