20 Let $P(x)=2 x^{3}+4 x^{2}-8 x+5, Q(x)=9-8 x^{3}$ and $R(x)=-2 x^{2}+9 x-x^{3}+8$. Find the simplified expression of the following:
a $P(x)-R(x)$
b $P(x)-(R(x)-Q(x))$

Step 1 ：Let $P(x)=2 x^{3}+4 x^{2}-8 x+5, Q(x)=9-8 x^{3}$ and $R(x)=-2 x^{2}+9 x-x^{3}+8$. We are asked to find the simplified expression of $P(x)-R(x)$ and $P(x)-(R(x)-Q(x))$.

Step 2 ：First, we find $P(x)-R(x)$. To do this, we subtract the corresponding coefficients of the same degree terms in $R(x)$ from $P(x)$. This gives us $3x^3 + 6x^2 - 17x - 3$.

Step 3 ：Next, we find $P(x)-(R(x)-Q(x))$. To do this, we subtract the expression $R(x)-Q(x)$ from $P(x)$. This gives us $-5x^3 + 6x^2 - 17x + 6$.

Step 4 ：Final Answer: The simplified expressions are a) $P(x)-R(x) = \boxed{3x^3 + 6x^2 - 17x - 3}$ and b) $P(x)-(R(x)-Q(x)) = \boxed{-5x^3 + 6x^2 - 17x + 6}$