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