Simplify (x^3-3x+1)-(x^3+7-12x)

$(x^{3} - 3 x + 1) - (x^{3} + 7 - 12 x)$

Simplify each term.

Apply the distributive property.

$x^{3} - 3 x + 1 - x^{3} - 1 \cdot 7 - (- 12 x)$

Simplify.

Multiply $- 1$ by $7$ .

$x^{3} - 3 x + 1 - x^{3} - 7 - (- 12 x)$

Multiply $- 12$ by $- 1$ .

$x^{3} - 3 x + 1 - x^{3} - 7 + 12 x$

Simplify by adding terms.

Combine the opposite terms in $x^{3} - 3 x + 1 - x^{3} - 7 + 12 x$ .

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

$- 3 x + 1 + 0 - 7 + 12 x$

Add $- 3 x + 1$ and $0$ .

$- 3 x + 1 - 7 + 12 x$

Add $- 3 x$ and $12 x$ .

$9 x + 1 - 7$

Subtract $7$ from $1$ .

$9 x - 6$