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

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

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $2$ by $- 1$ .

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

Multiply $- 2$ by $- 1$ .

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

Multiply $- 3$ by $- 1$ .

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

Multiply $4$ by $- 1$ .

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

Remove parentheses.

$4 x y + 3 x^{2} y - 2 x y^{2} + 3 y - 2 x y + 2 x^{2} y + 3 x y^{2} - 4 x$

Simplify by adding terms.

Subtract $2 x y$ from $4 x y$ .

$2 x y + 3 x^{2} y - 2 x y^{2} + 3 y + 2 x^{2} y + 3 x y^{2} - 4 x$

Add $3 x^{2} y$ and $2 x^{2} y$ .

$2 x y + 5 x^{2} y - 2 x y^{2} + 3 y + 3 x y^{2} - 4 x$

Add $- 2 x y^{2}$ and $3 x y^{2}$ .

$2 x y + 5 x^{2} y + 1 x y^{2} + 3 y - 4 x$

Simplify the expression.

Multiply $x$ by $1$ .

$2 x y + 5 x^{2} y + x y^{2} + 3 y - 4 x$

Move $3 y$ .

$2 x y + 5 x^{2} y + x y^{2} - 4 x + 3 y$

Move $2 x y$ .

$5 x^{2} y + x y^{2} + 2 x y - 4 x + 3 y$