Answer
$-2x^{3}+8x^{2}-19x-2$
Work Step by Step
We are asked to subtract $(9x+8)$ from the sum of $(3x^{2}-2x-x^{3}+2)$ and $(5x^{2}-8x-x^{3}+4)$. This is equivalent to the expression $(3x^{2}-2x-x^{3}+2)+(5x^{2}-8x-x^{3}+4)-(9x+8)$.
We can subtract the third term from the first two terms by adding the opposite of the third term to the first two.
$(3x^{2}-2x-x^{3}+2)+(5x^{2}-8x-x^{3}+4)+(-9x-8)$
Next, we can combine like terms.
$(-x^{3}-x^{3})+(3x^{2}+5x^{2})+(-2x-8x-9x)+(2+4-8)=-2x^{3}+8x^{2}-19x-2$
