Evaluate: (x^3-3x+1)-(x^3+7-12x)

Expression: $\left( {x}^{3}-3x+1 \right)-\left( {x}^{3}+7-12x \right)$

Remove unnecessary parentheses

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

When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses

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

Since two opposites add up to $0$, remove them from the expression

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

Collect like terms

$9x+1-7$

Calculate the difference

$9x-6$