TITLE: Given $f(x)$ and $g(x)$, find $(fg)(x)$
QUESTION [6 upvotes]: I've attempted to solve the problem below, and here is what I got for a solution:

Given $f(x)=x^2-9$ and $g(x)=x^2+3x-1$, find $(fg)(x).$

$$
\begin{align}
(fg)(x)&=(x^2-9)(x^2+3x-1)\\
&=x^4+3x^3-x^2-9x^2-27x+9\\
&=x^4+3x^3-10x^2-27x+9
\end{align}
$$
Have I done this correctly?
I am wondering if I should have factored $(x^2-9)$ before multiplying, but I'm not sure if it would have made a difference.

REPLY [7 votes]: You are correct. If I know what you are saying, you are right that it wouldn't matter. The factored form is $(x+3)(x-3)(x^2+3x-1)$.