Where am I going wrong when removing brackets from (s+1)(s+5)(s-3) One of my text book exercises is to remove the brackets from this expression:
$ (s+1)(s+5)(s-3) $
The I've tried a number of times and the result I keep getting is:
$ s^3 -3s^2 -13s -15 $
However, my textbook says the answer is:
$ s^2 -3s^2 -13s -15 $
I keep getting the same answer, but I'm reluctant to think the text book is wrong. 
Here's how I come to that result:
$ (s+1)(s+5)(s-3)$ 
$ = s((s+1)(s+5)) - 3((s+1)(s+5))$
$ = s(s(s+1) + 5(s+1)) - 3(s(s+1) + 5(s+1))$
$ = s(s^2 + s + 5s + 5) - 3(s^2 + s + 5s + 5)$
$ = s^3 + s^2 + 5s^2 + 5s - 3s^2 -3s -15s -15$
Then re-arrange that to:
$ = s^3 +6s^2 - 3s^2  + 5s - 3s -15s -15$
And my final answer (Updated to reflect jorikis answer below):
$ s^3 +3s^2 -13s -15 $
Any advice greatly appreciated.
 A: Neither of these results is correct; the correct result is $s^3+3s^2-13s-15$. The error in your calculation is where you replace $6s^2-3s^2$ by $-3s^2$.
A: The error is, in fact, in your textbook: The product $(s+1)(s+5)(s-3)$ will, after expansion, have a term $s^3$ in it (as in your result). Since it is missing in the textbook, the answer given there is wrong.
On the other hand, your derivation looks fine to me, so I would say that you are right and the textbook has a typo in it.
Edit: In fact, there is an error in your calculation; see the other answer. Still, the textbook answer is wrong.
A: $1$.  The textbook answer obviously has a typo. It is highly implausible that anyone would intend $ s^2 -3s^2 -13s -15 $ as a final answer.
$2.$  While you were doing the calculation, you had the intermediate expression 
$ s(s^2 + s + 5s + 5) - 3(s^2 + s + 5s + 5)$, and then multiplied without changing the $s^2+s+5s+5$ automatically to $s^2+6s+5$. The more terms you have, the more work you need to do. Each step up in complexity introduces new opportunities for error.
$3.$  I would have as a matter of strategy preferred to find $(s+5)(s-3)$ first, since multiplying by $s+1$ is more pleasant than multiplying by $s-3$.
$4.$  Any calculation involves the possibility of computational error, or error in writing down the result of the computation. It is not a bad idea to make a final plausibility scan, like evaluating the original expression and the expanded one at some nice number, such as $x=1$.  
$5.$ You have undoubtedly acquired visual shortcuts for expanding things like $(x+a)(x+b)$, and even $(px+a)(qx+b)$.  Note that $(x+a)(x+b)(x+c)=x^3+(a+b+c)x^2+(ab+bc+ca)x+abc$.   
