Simplify (4xy^2+3x^2y^2-2x^2y+6)-(3xy^2+2x^2y+4x^2y^2-1)

$(4 x y^{2} + 3 x^{2} y^{2} - 2 x^{2} y + 6) - (3 x y^{2} + 2 x^{2} y + 4 x^{2} y^{2} - 1)$

Simplify each term.

Apply the distributive property.

$4 x y^{2} + 3 x^{2} y^{2} - 2 x^{2} y + 6 - (3 x y^{2}) - (2 x^{2} y) - (4 x^{2} y^{2}) - - 1$

Simplify.

Multiply $3$ by $- 1$ .

$4 x y^{2} + 3 x^{2} y^{2} - 2 x^{2} y + 6 - 3 (x y^{2}) - (2 x^{2} y) - (4 x^{2} y^{2}) - - 1$

Multiply $2$ by $- 1$ .

$4 x y^{2} + 3 x^{2} y^{2} - 2 x^{2} y + 6 - 3 (x y^{2}) - 2 (x^{2} y) - (4 x^{2} y^{2}) - - 1$

Multiply $4$ by $- 1$ .

$4 x y^{2} + 3 x^{2} y^{2} - 2 x^{2} y + 6 - 3 (x y^{2}) - 2 (x^{2} y) - 4 (x^{2} y^{2}) - - 1$

Multiply $- 1$ by $- 1$ .

$4 x y^{2} + 3 x^{2} y^{2} - 2 x^{2} y + 6 - 3 (x y^{2}) - 2 (x^{2} y) - 4 (x^{2} y^{2}) + 1$

Remove parentheses.

$4 x y^{2} + 3 x^{2} y^{2} - 2 x^{2} y + 6 - 3 x y^{2} - 2 x^{2} y - 4 x^{2} y^{2} + 1$

Simplify by adding terms.

Subtract $3 x y^{2}$ from $4 x y^{2}$ .

$1 x y^{2} + 3 x^{2} y^{2} - 2 x^{2} y + 6 - 2 x^{2} y - 4 x^{2} y^{2} + 1$

Multiply $x$ by $1$ .

$x y^{2} + 3 x^{2} y^{2} - 2 x^{2} y + 6 - 2 x^{2} y - 4 x^{2} y^{2} + 1$

Subtract $4 x^{2} y^{2}$ from $3 x^{2} y^{2}$ .

$x y^{2} - x^{2} y^{2} - 2 x^{2} y + 6 - 2 x^{2} y + 1$

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

$x y^{2} - x^{2} y^{2} - 4 x^{2} y + 6 + 1$

Add $6$ and $1$ .

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