Question 4: Factorize:
\((i)\) \(\;\) \( 125a^3-1\)
Solution:
$\displaystyle \ \ \ \ 125a^{3} -1$
$\displaystyle =( 5a)^{3} -1^{3}$
$\displaystyle =( 5a-1)\left[( 5a)^{2} +( 5a)( 1) +1^{2}\right]$
$\displaystyle =( 5a-1)\left( 25a^{2} +5a+1\right)$
Question 4: Factorize:
\((i)\) \(\;\) \( 125a^3-1\)
Solution:
$\displaystyle \ \ \ \ 125a^{3} -1$
$\displaystyle =( 5a)^{3} -1^{3}$
$\displaystyle =( 5a-1)\left[( 5a)^{2} +( 5a)( 1) +1^{2}\right]$
$\displaystyle =( 5a-1)\left( 25a^{2} +5a+1\right)$