Answer:
To simplify the expression, we need to distribute the negative sign to all the terms inside the parentheses, and then combine like terms.
Starting with:
(5x^4-4x^3-2x^2+x-19)-(x^4+5x^3+8x^2+x+5)
Distribute the negative sign inside the parentheses:
5x^4 - 4x^3 - 2x^2 + x - 19 - x^4 - 5x^3 - 8x^2 - x - 5
Now we can combine like terms:
(5x^4 - x^4) + (-4x^3 - 5x^3) + (-2x^2 - 8x^2) + (x - x) + (-19 - 5)
Simplifying further:
4x^4 - 9x^3 - 10x^2 - 24
Therefore, the simplified expression is:
4x^4 - 9x^3 - 10x^2 - 24.