Question
Factorize:
$x^3 - 2x^2y + 3xy^2 - 6y^3$
$x^3 - 2x^2y + 3xy^2 - 6y^3$
✓
Answer
$x^3-2 x^2 y+3 x y^2-6 y^3$
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 $(x-2 y)$
common in the terms $=(x-2 y)\left(x^2+3 y^2\right)$
$\therefore x^3-2 x^2 y+3 x y^2-6 y^3=(x-2 y)\left(x^2+3 y^2\right)$
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 $(x-2 y)$
common in the terms $=(x-2 y)\left(x^2+3 y^2\right)$
$\therefore x^3-2 x^2 y+3 x y^2-6 y^3=(x-2 y)\left(x^2+3 y^2\right)$
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