Simplify (5x^4-4x^3-2x^2+x-19)-(x^4+5x^3+8x^2+x+5)

$(5 x^{4} - 4 x^{3} - 2 x^{2} + x - 19) - (x^{4} + 5 x^{3} + 8 x^{2} + x + 5)$

Simplify each term.

Apply the distributive property.

$5 x^{4} - 4 x^{3} - 2 x^{2} + x - 19 - x^{4} - (5 x^{3}) - (8 x^{2}) - x - 1 \cdot 5$

Simplify.

Multiply $5$ by $- 1$ .

$5 x^{4} - 4 x^{3} - 2 x^{2} + x - 19 - x^{4} - 5 x^{3} - (8 x^{2}) - x - 1 \cdot 5$

Multiply $8$ by $- 1$ .

$5 x^{4} - 4 x^{3} - 2 x^{2} + x - 19 - x^{4} - 5 x^{3} - 8 x^{2} - x - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$5 x^{4} - 4 x^{3} - 2 x^{2} + x - 19 - x^{4} - 5 x^{3} - 8 x^{2} - x - 5$

Simplify by adding terms.

Combine the opposite terms in $5 x^{4} - 4 x^{3} - 2 x^{2} + x - 19 - x^{4} - 5 x^{3} - 8 x^{2} - x - 5$ .

Subtract $x$ from $x$ .

$5 x^{4} - 4 x^{3} - 2 x^{2} - 19 - x^{4} - 5 x^{3} - 8 x^{2} + 0 - 5$

Add $5 x^{4} - 4 x^{3} - 2 x^{2} - 19 - x^{4} - 5 x^{3} - 8 x^{2}$ and $0$ .

$5 x^{4} - 4 x^{3} - 2 x^{2} - 19 - x^{4} - 5 x^{3} - 8 x^{2} - 5$

Subtract $x^{4}$ from $5 x^{4}$ .

$4 x^{4} - 4 x^{3} - 2 x^{2} - 19 - 5 x^{3} - 8 x^{2} - 5$

Subtract $5 x^{3}$ from $- 4 x^{3}$ .

$4 x^{4} - 9 x^{3} - 2 x^{2} - 19 - 8 x^{2} - 5$

Subtract $8 x^{2}$ from $- 2 x^{2}$ .

$4 x^{4} - 9 x^{3} - 10 x^{2} - 19 - 5$

Subtract $5$ from $- 19$ .

$4 x^{4} - 9 x^{3} - 10 x^{2} - 24$