Simplify (x^2+6x^3+3)-(3x^3+6x^2-3-4x)

$(x^{2} + 6 x^{3} + 3) - (3 x^{3} + 6 x^{2} - 3 - 4 x)$

Simplify each term.

Apply the distributive property.

$x^{2} + 6 x^{3} + 3 - (3 x^{3}) - (6 x^{2}) - - 3 - (- 4 x)$

Simplify.

Multiply $3$ by $- 1$ .

$x^{2} + 6 x^{3} + 3 - 3 x^{3} - (6 x^{2}) - - 3 - (- 4 x)$

Multiply $6$ by $- 1$ .

$x^{2} + 6 x^{3} + 3 - 3 x^{3} - 6 x^{2} - - 3 - (- 4 x)$

Multiply $- 1$ by $- 3$ .

$x^{2} + 6 x^{3} + 3 - 3 x^{3} - 6 x^{2} + 3 - (- 4 x)$

Multiply $- 4$ by $- 1$ .

$x^{2} + 6 x^{3} + 3 - 3 x^{3} - 6 x^{2} + 3 + 4 x$

Simplify by adding terms.

Subtract $6 x^{2}$ from $x^{2}$ .

$6 x^{3} + 3 - 3 x^{3} - 5 x^{2} + 3 + 4 x$

Subtract $3 x^{3}$ from $6 x^{3}$ .

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

Simplify the expression.

Add $3$ and $3$ .

$3 x^{3} - 5 x^{2} + 6 + 4 x$

Move $6$ .

$3 x^{3} - 5 x^{2} + 4 x + 6$