Question:
Factorize: \[ x^3-2x^2y+3xy^2-6y^3 \]
Solution:
\[ x^3-2x^2y+3xy^2-6y^3 \]
\[ =x^2(x-2y)+3y^2(x-2y) \]
\[ =(x-2y)(x^2+3y^2) \]
\[ \boxed{(x-2y)(x^2+3y^2)} \]
Factorize: \[ x^3-2x^2y+3xy^2-6y^3 \]
\[ x^3-2x^2y+3xy^2-6y^3 \]
\[ =x^2(x-2y)+3y^2(x-2y) \]
\[ =(x-2y)(x^2+3y^2) \]
\[ \boxed{(x-2y)(x^2+3y^2)} \]