Question:
Find the value
$x^{3}-2 x^{2} b+3 x y^{2}-6 y^{3}$
Solution:
Taking $x^{2}$ common in $\left(x^{3}-2 x^{2} y\right)$ and $+3 y^{2}$ common in $\left(3 x y^{2}-6 y^{3}\right)$
$=x^{2}(x-2 y)+3 y^{2}(x-2 y)$
Taking (x - 2y) common in the terms
$=(x-2 y)\left(x^{2}+3 y^{2}\right)$
$\therefore x^{3}-2 x^{2} y+3 x y^{2}-6 y^{3}=(x-2 y)\left(x^{2}+3 y^{2}\right)$