Question

Factorize:
x³ − 2x²y + 3xy² − 6y³

Answer 1

We have:
$x^3-2x^{2}y+3x{y}^2-6y^3=\left(x^3-2x^{2}y\right)+\left(3x{y}^2-6y^3\right)$
$$\begin{gathered} =x^2\left(x-2y\right)+3y^2\left(x-2y\right) \\ =\left(x-2y\right)\left(x^2+3y^2\right) \end{gathered}$$