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

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

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $- 3$ by $- 1$ .

$x^{3} + 2 x^{2} - x + 4 - x^{3} + 3 x^{2} - 1 \cdot 3$

Multiply $- 1$ by $3$ .

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

Simplify by adding terms.

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

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

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

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

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

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

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

Subtract $3$ from $4$ .

$5 x^{2} - x + 1$