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.