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

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

Step 1

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $- 9$ by $- 1$ .

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

Multiply $- 3$ by $- 1$ .

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

Multiply $4$ by $- 1$ .

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

Multiply $- 1$ by $9$ .

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

Step 2

Simplify by adding terms.

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

$13 x^{4} + 2 y^{3} - 6 z^{3} + 4 + 3 y^{3} - 4 z^{3} - 9$

Add $2 y^{3}$ and $3 y^{3}$ .

$13 x^{4} + 5 y^{3} - 6 z^{3} + 4 - 4 z^{3} - 9$

Subtract $4 z^{3}$ from $- 6 z^{3}$ .

$13 x^{4} + 5 y^{3} - 10 z^{3} + 4 - 9$

Subtract $9$ from $4$ .

$13 x^{4} + 5 y^{3} - 10 z^{3} - 5$