Question

Factorize each of the following expressions:
x³ − 2x²y + 3xy² − 6y³

Answer 1

$$\begin{gathered} x^3{-\; 2x}^2{\mathrm{y\; +\; 3xy}}^2{-\; 6y}^3 \\ =(x^3-2x^{2}y)+(3x{y}^2-6y^3)[Groupingtheexpressions] \\ =x^2(x-2y)+3y^2(x-2y) \\ =(x^2+3y^2)(x-2y)[Taking(x-2y)asthecommonfactor] \end{gathered}$$