If $X$ has mean $3$ and variance $8$, find $E\left[(3 + 2X)^2\right]$ and $E(4 + 7X)$. this question is throwing me off and my textbook doesn't include any solutions, or any examples relating to these kinds of question so any help on a solutuion would be great
If $X$ has mean $3$ and variance $8$, find $E\left[(3 + 2X)^2\right]$ and $E(4 + 7X)$.

By linearity of $E$, 
$$\begin{align} E[(3+2X)^2]&=E[9+12X+4X^2]\\& = E[9]+E[12X]+E[4X^2]\\&=9+12E[X]+4E[X^2].\end{align}$$
Now recall that 
$$V[X] = E[X^2]-E[X]^2. $$
