Divide (4xy^2-2xy+2x^2y)/(xy)

$\frac{4 x y^{2} - 2 x y + 2 x^{2} y}{x y}$

Step 1

Factor $2 x y$ out of $4 x y^{2} - 2 x y + 2 x^{2} y$ .

Factor $2 x y$ out of $4 x y^{2}$ .

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

Factor $2 x y$ out of $- 2 x y$ .

$\frac{2 x y (2 y) + 2 x y (- 1) + 2 x^{2} y}{x y}$

Factor $2 x y$ out of $2 x^{2} y$ .

$\frac{2 x y (2 y) + 2 x y (- 1) + 2 x y (x)}{x y}$

Factor $2 x y$ out of $2 x y (2 y) + 2 x y (- 1)$ .

$\frac{2 x y (2 y - 1) + 2 x y (x)}{x y}$

Factor $2 x y$ out of $2 x y (2 y - 1) + 2 x y (x)$ .

$\frac{2 x y (2 y - 1 + x)}{x y}$

Step 2

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{2 x y (2 y - 1 + x)}{x y}$

Rewrite the expression.

$\frac{2 y (2 y - 1 + x)}{y}$

Step 3

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{2 y (2 y - 1 + x)}{y}$

Divide $2 (2 y - 1 + x)$ by $1$ .

$2 (2 y - 1 + x)$

Step 4

Apply the distributive property.

$2 (2 y) + 2 \cdot - 1 + 2 x$

Step 5

Simplify.

Multiply $2$ by $2$ .

$4 y + 2 \cdot - 1 + 2 x$

Multiply $2$ by $- 1$ .

$4 y - 2 + 2 x$