Simplify (16x^2y^3-2x^3y^2+4x^2y^2+4xy)/(2xy)

$\frac{16 x^{2} y^{3} - 2 x^{3} y^{2} + 4 x^{2} y^{2} + 4 x y}{2 x y}$

Step 1

Factor $2 x y$ out of $16 x^{2} y^{3} - 2 x^{3} y^{2} + 4 x^{2} y^{2} + 4 x y$ .

Factor $2 x y$ out of $16 x^{2} y^{3}$ .

$\frac{2 x y (8 x y^{2}) - 2 x^{3} y^{2} + 4 x^{2} y^{2} + 4 x y}{2 x y}$

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

$\frac{2 x y (8 x y^{2}) + 2 x y (- x^{2} y) + 4 x^{2} y^{2} + 4 x y}{2 x y}$

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

$\frac{2 x y (8 x y^{2}) + 2 x y (- x^{2} y) + 2 x y (2 x y) + 4 x y}{2 x y}$

Factor $2 x y$ out of $4 x y$ .

$\frac{2 x y (8 x y^{2}) + 2 x y (- x^{2} y) + 2 x y (2 x y) + 2 x y (2)}{2 x y}$

Factor $2 x y$ out of $2 x y (8 x y^{2}) + 2 x y (- x^{2} y)$ .

$\frac{2 x y (8 x y^{2} - x^{2} y) + 2 x y (2 x y) + 2 x y (2)}{2 x y}$

Factor $2 x y$ out of $2 x y (8 x y^{2} - x^{2} y) + 2 x y (2 x y)$ .

$\frac{2 x y (8 x y^{2} - x^{2} y + 2 x y) + 2 x y (2)}{2 x y}$

Factor $2 x y$ out of $2 x y (8 x y^{2} - x^{2} y + 2 x y) + 2 x y (2)$ .

$\frac{2 x y (8 x y^{2} - x^{2} y + 2 x y + 2)}{2 x y}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x y (8 x y^{2} - x^{2} y + 2 x y + 2)}{2 x y}$

Rewrite the expression.

$\frac{x y (8 x y^{2} - x^{2} y + 2 x y + 2)}{x y}$

Step 3

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x y (8 x y^{2} - x^{2} y + 2 x y + 2)}{x y}$

Rewrite the expression.

$\frac{y (8 x y^{2} - x^{2} y + 2 x y + 2)}{y}$

Step 4

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{y (8 x y^{2} - x^{2} y + 2 x y + 2)}{y}$

Divide $8 x y^{2} - x^{2} y + 2 x y + 2$ by $1$ .

$8 x y^{2} - x^{2} y + 2 x y + 2$