Simplify (-2x^4-5+4x+2x^3)-(2x^3-8x^4-4x+8)

$(- 2 x^{4} - 5 + 4 x + 2 x^{3}) - (2 x^{3} - 8 x^{4} - 4 x + 8)$

Simplify each term.

Apply the distributive property.

$- 2 x^{4} - 5 + 4 x + 2 x^{3} - (2 x^{3}) - (- 8 x^{4}) - (- 4 x) - 1 \cdot 8$

Simplify.

Multiply $2$ by $- 1$ .

$- 2 x^{4} - 5 + 4 x + 2 x^{3} - 2 x^{3} - (- 8 x^{4}) - (- 4 x) - 1 \cdot 8$

Multiply $- 8$ by $- 1$ .

$- 2 x^{4} - 5 + 4 x + 2 x^{3} - 2 x^{3} + 8 x^{4} - (- 4 x) - 1 \cdot 8$

Multiply $- 4$ by $- 1$ .

$- 2 x^{4} - 5 + 4 x + 2 x^{3} - 2 x^{3} + 8 x^{4} + 4 x - 1 \cdot 8$

Multiply $- 1$ by $8$ .

$- 2 x^{4} - 5 + 4 x + 2 x^{3} - 2 x^{3} + 8 x^{4} + 4 x - 8$

Simplify by adding terms.

Combine the opposite terms in $- 2 x^{4} - 5 + 4 x + 2 x^{3} - 2 x^{3} + 8 x^{4} + 4 x - 8$ .

Subtract $2 x^{3}$ from $2 x^{3}$ .

$- 2 x^{4} - 5 + 4 x + 0 + 8 x^{4} + 4 x - 8$

Add $- 2 x^{4} - 5 + 4 x$ and $0$ .

$- 2 x^{4} - 5 + 4 x + 8 x^{4} + 4 x - 8$

Add $- 2 x^{4}$ and $8 x^{4}$ .

$6 x^{4} - 5 + 4 x + 4 x - 8$

Subtract $8$ from $- 5$ .

$6 x^{4} + 4 x + 4 x - 13$

Add $4 x$ and $4 x$ .

$6 x^{4} + 8 x - 13$