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

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

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $- 3$ by $- 1$ .

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

Multiply $3$ by $- 1$ .

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

Multiply $2$ by $- 1$ .

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

Multiply $- 2$ by $- 1$ .

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

Remove parentheses.

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

Simplify by adding terms.

Combine the opposite terms in $4 x^{2} y^{2} + 3 x^{2} y - 2 x y^{2} + 4 x y + 3 x^{2} y^{2} - 3 x^{2} y - 2 x y^{2} + 2 x y$ .

Subtract $3 x^{2} y$ from $3 x^{2} y$ .

$4 x^{2} y^{2} - 2 x y^{2} + 4 x y + 3 x^{2} y^{2} + 0 - 2 x y^{2} + 2 x y$

Add $4 x^{2} y^{2} - 2 x y^{2} + 4 x y + 3 x^{2} y^{2}$ and $0$ .

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

Add $4 x^{2} y^{2}$ and $3 x^{2} y^{2}$ .

$7 x^{2} y^{2} - 2 x y^{2} + 4 x y - 2 x y^{2} + 2 x y$

Subtract $2 x y^{2}$ from $- 2 x y^{2}$ .

$7 x^{2} y^{2} - 4 x y^{2} + 4 x y + 2 x y$

Add $4 x y$ and $2 x y$ .

$7 x^{2} y^{2} - 4 x y^{2} + 6 x y$