Factor x^3(2x-y)+xy(2x-y)^2

$x^{3} (2 x - y) + x y {(2 x - y)}^{2}$

Factor $x (2 x - y)$ out of $x^{3} (2 x - y) + x y {(2 x - y)}^{2}$ .

Factor $x (2 x - y)$ out of $x^{3} (2 x - y)$ .

$x (2 x - y) (x^{2}) + x y {(2 x - y)}^{2}$

Factor $x (2 x - y)$ out of $x y {(2 x - y)}^{2}$ .

$x (2 x - y) (x^{2}) + x (2 x - y) (y (2 x - y))$

Factor $x (2 x - y)$ out of $x (2 x - y) (x^{2}) + x (2 x - y) (y (2 x - y))$ .

$x (2 x - y) (x^{2} + y (2 x - y))$

Apply the distributive property.

$x (2 x - y) (x^{2} + y (2 x) + y (- y))$

Rewrite using the commutative property of multiplication.

$x (2 x - y) (x^{2} + 2 y x + y (- y))$

Rewrite using the commutative property of multiplication.

$x (2 x - y) (x^{2} + 2 y x - y \cdot y)$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$x (2 x - y) (x^{2} + 2 y x - (y \cdot y))$

Multiply $y$ by $y$ .

$x (2 x - y) (x^{2} + 2 y x - y^{2})$