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

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

Remove parentheses.

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

Simplify each term.

Apply the distributive property.

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

Multiply $- (- x y)$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Apply the distributive property.

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

Multiply $- 3$ by $- 1$ .

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

Simplify by adding terms.

Subtract $x^{2}$ from $4 x^{2}$ .

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

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

$6 x^{2} + x y - 3 y^{2} + 2 x y - y^{2}$

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

$6 x^{2} - 3 y^{2} + 3 x y - y^{2}$

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

$6 x^{2} - 4 y^{2} + 3 x y$