Simplify (-2x^4-4y^3+4z^3+6)-(-9x^4-3y^3+4z^3+9)

$(- 2 x^{4} - 4 y^{3} + 4 z^{3} + 6) - (- 9 x^{4} - 3 y^{3} + 4 z^{3} + 9)$

Simplify each term.

Apply the distributive property.

$- 2 x^{4} - 4 y^{3} + 4 z^{3} + 6 - (- 9 x^{4}) - (- 3 y^{3}) - (4 z^{3}) - 1 \cdot 9$

Simplify.

Multiply $- 9$ by $- 1$ .

$- 2 x^{4} - 4 y^{3} + 4 z^{3} + 6 + 9 x^{4} - (- 3 y^{3}) - (4 z^{3}) - 1 \cdot 9$

Multiply $- 3$ by $- 1$ .

$- 2 x^{4} - 4 y^{3} + 4 z^{3} + 6 + 9 x^{4} + 3 y^{3} - (4 z^{3}) - 1 \cdot 9$

Multiply $4$ by $- 1$ .

$- 2 x^{4} - 4 y^{3} + 4 z^{3} + 6 + 9 x^{4} + 3 y^{3} - 4 z^{3} - 1 \cdot 9$

Multiply $- 1$ by $9$ .

$- 2 x^{4} - 4 y^{3} + 4 z^{3} + 6 + 9 x^{4} + 3 y^{3} - 4 z^{3} - 9$

Simplify by adding terms.

Combine the opposite terms in $- 2 x^{4} - 4 y^{3} + 4 z^{3} + 6 + 9 x^{4} + 3 y^{3} - 4 z^{3} - 9$ .

Subtract $4 z^{3}$ from $4 z^{3}$ .

$- 2 x^{4} - 4 y^{3} + 6 + 9 x^{4} + 3 y^{3} + 0 - 9$

Add $- 2 x^{4} - 4 y^{3} + 6 + 9 x^{4} + 3 y^{3}$ and $0$ .

$- 2 x^{4} - 4 y^{3} + 6 + 9 x^{4} + 3 y^{3} - 9$

Add $- 2 x^{4}$ and $9 x^{4}$ .

$7 x^{4} - 4 y^{3} + 6 + 3 y^{3} - 9$

Add $- 4 y^{3}$ and $3 y^{3}$ .

$7 x^{4} - y^{3} + 6 - 9$

Subtract $9$ from $6$ .

$7 x^{4} - y^{3} - 3$