Question 4: Factorize:
\((iii)\) \(\;\) \(x^6-27 \)
Solution:
$\displaystyle\ \ \ \ x^{6} -27$
$\displaystyle =\left( x^{2}\right)^{3} -3^{3}$
$\displaystyle =\left( x^{2} -3\right)\left[\left( x^{2}\right)^{2} +\left( x^{2}\right)( 3) +3^{2}\right]$
$\displaystyle =\left( x^{2} -3\right)\left( x^{4} +3x^{2} +9\right)$