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

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

Step 1

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $- 4$ by $- 1$ .

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

Multiply $2$ by $- 1$ .

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

Multiply $3$ by $- 1$ .

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

Remove parentheses.

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

Step 2

Simplify by adding terms.

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

$8 x^{2} y - 3 x y^{2} + 4 x - 3 x y - 2 x y - 3 x y^{2} - x$

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

$8 x^{2} y - 6 x y^{2} + 4 x - 3 x y - 2 x y - x$

Subtract $x$ from $4 x$ .

$8 x^{2} y - 6 x y^{2} - 3 x y - 2 x y + 3 x$

Subtract $2 x y$ from $- 3 x y$ .

$8 x^{2} y - 6 x y^{2} - 5 x y + 3 x$