Question 4: Factorize:
\((iv)\) \(\; \)\(1000a^3+1 \)
Solution:
$\displaystyle \ \ \ \ 1000a^{3} +1$
$\displaystyle =( 10a)^{3} +1^{3}$
$\displaystyle =( 10a+1)\left[( 10a)^{2} -( 10a)( 1) +1^{2}\right]$
$\displaystyle =( 10a+1)\left( 100a^{2} -10a+1\right)$