Simplify (3a^2-a+2)+(-3a^2+3a-1)-(a^2-1)

$(3 a^{2} - a + 2) + (- 3 a^{2} + 3 a - 1) - (a^{2} - 1)$

Simplify by adding terms.

Remove parentheses.

$3 a^{2} - a + 2 - 3 a^{2} + 3 a - 1 - (a^{2} - 1)$

Combine the opposite terms in $3 a^{2} - a + 2 - 3 a^{2} + 3 a - 1 - (a^{2} - 1)$ .

Subtract $3 a^{2}$ from $3 a^{2}$ .

$- a + 2 + 0 + 3 a - 1 - (a^{2} - 1)$

Add $- a + 2$ and $0$ .

$- a + 2 + 3 a - 1 - (a^{2} - 1)$

Simplify each term.

Apply the distributive property.

$- a + 2 + 3 a - 1 - a^{2} - - 1$

Multiply $- 1$ by $- 1$ .

$- a + 2 + 3 a - 1 - a^{2} + 1$

Simplify by adding terms.

Combine the opposite terms in $- a + 2 + 3 a - 1 - a^{2} + 1$ .

Add $- 1$ and $1$ .

$- a + 2 + 3 a - a^{2} + 0$

Add $- a + 2 + 3 a - a^{2}$ and $0$ .

$- a + 2 + 3 a - a^{2}$

Add $- a$ and $3 a$ .

$2 a + 2 - a^{2}$

Simplify the expression.

Move $2$ .

$2 a - a^{2} + 2$

Reorder $2 a$ and $- a^{2}$ .

$- a^{2} + 2 a + 2$