Question 3: Factorize:
\((iii)\) \(\;\) \(x^3+48x^2y+108xy^2+216y^3 \)
Note: The question given in the book is incorrect. The correct form of the question should be: \(x^3+18x^2y+108xy^2+216y^3 \)
Solution:
$\displaystyle \ \ \ \ x^{3} +18x^{2} y+108xy^{2} +216y^{3}$
$\displaystyle =( x)^{3} +3( x)^{2}( 6y) +3( x)( 6y)^{2} +( 6y)^{3}$
$\displaystyle =( x+6y)^{3}$