Simplify (5x-12x^2+9x^3)-(5x^3+6x-3)

$(5 x - 12 x^{2} + 9 x^{3}) - (5 x^{3} + 6 x - 3)$

Simplify each term.

Apply the distributive property.

$5 x - 12 x^{2} + 9 x^{3} - (5 x^{3}) - (6 x) - - 3$

Simplify.

Multiply $5$ by $- 1$ .

$5 x - 12 x^{2} + 9 x^{3} - 5 x^{3} - (6 x) - - 3$

Multiply $6$ by $- 1$ .

$5 x - 12 x^{2} + 9 x^{3} - 5 x^{3} - 6 x - - 3$

Multiply $- 1$ by $- 3$ .

$5 x - 12 x^{2} + 9 x^{3} - 5 x^{3} - 6 x + 3$

Simplify by adding terms.

Subtract $6 x$ from $5 x$ .

$- 12 x^{2} + 9 x^{3} - 5 x^{3} - x + 3$

Subtract $5 x^{3}$ from $9 x^{3}$ .

$- 12 x^{2} + 4 x^{3} - x + 3$

Reorder $- 12 x^{2}$ and $4 x^{3}$ .

$4 x^{3} - 12 x^{2} - x + 3$