Factorize each of the following expression:
(3x + 4y)4 − x4
$(3 x+4 y)^{4}-x^{4}$
$=\left[(3 x+4 y)^{2}\right]^{2}-\left(x^{2}\right)^{2}$
$=\left[(3 x+4 y)^{2}+x^{2}\right]\left[(3 x+4 y)^{2}-x^{2}\right]$
$=\left[(3 x+4 y)^{2}+x^{2}\right][(3 x+4 y)+x][(3 x+4 y)-x]$
$=\left\{(3 \mathrm{x}+4 \mathrm{y})^{2}+\mathrm{x}^{2}\right\}(3 \mathrm{x}+4 \mathrm{y}+\mathrm{x})(3 \mathrm{x}+4 \mathrm{y}-\mathrm{x})$
$=\left\{(3 \mathrm{x}+4 \mathrm{y})^{2}+\mathrm{x}^{2}\right\}(4 \mathrm{x}+4 \mathrm{y})(2 \mathrm{x}+4 \mathrm{y})$
$=\left\{(3 \mathrm{x}+4 \mathrm{y})^{2}+\mathrm{x}^{2}\right\} 4(\mathrm{x}+\mathrm{y}) 2(\mathrm{x}+2 \mathrm{y})$
$=8\left\{(3 \mathrm{x}+4 \mathrm{y})^{2}+\mathrm{x}^{2}\right\}(\mathrm{x}+\mathrm{y})(\mathrm{x}+2 \mathrm{y})$
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