Factorize each of the following algebraic expression:

$4 x^{4}+y^{4}$

$=4 \mathrm{x}^{4}+4 \mathrm{x}^{2} \mathrm{y}^{2}+\mathrm{y}^{4}-4 \mathrm{x}^{2} \mathrm{y}^{2}$

$=\left[\left(2 \mathrm{x}^{2}\right)^{2}+2 \times 2 \mathrm{x}^{2} \times \mathrm{y}+\left(\mathrm{y}^{2}\right)^{2}\right]-(2 \mathrm{xy})^{2}$

$=\left(2 \mathrm{x}^{2}+\mathrm{y}^{2}\right)^{2}-(2 \mathrm{xy})^{2}$

$=\left[\left(2 \mathrm{x}^{2}+\mathrm{y}^{2}\right)-2 \mathrm{xy}\right]\left[\left(2 \mathrm{x}^{2}+\mathrm{y}^{2}\right)+2 \mathrm{xy}\right]$

$=\left(2 \mathrm{x}^{2}-2 \mathrm{xy}+\mathrm{y}^{2}\right)\left(2 \mathrm{x}^{2}+2 \mathrm{xy}+\mathrm{y}^{2}\right)$