Question:
Factorize each of the following expressions:
x3 − 2x2y + 3xy2 − 6y3
Solution:
$x^{3}-2 \mathrm{x}^{2} \mathrm{y}+3 \mathrm{xy}^{2}-6 \mathrm{y}^{3}$
$=\left(x^{3}-2 x^{2} y\right)+\left(3 x y^{2}-6 y^{3}\right)$ [Grouping the expressions]
$=x^{2}(x-2 y)+3 y^{2}(x-2 y)$
$=\left(x^{2}+3 y^{2}\right)(x-2 y)$ $[$ Taking $(x-2 y)$ as the common factor $]$