Can anyone help me with this? The question asks to differentiate the following...

(x-5)^8 * (x+3)^6

The way I attempted it was to try using the product rule, but I don't get the same answer as stated in the book.

I used the chain rule to differentiate each of the two arguments, getting 8(x-5)^7 and 6(x+3)^5 respectively. At that point I attempted to use the product rule, getting:

8(x-5)^7*(x+3)^6 + (x-5)^8*6(x+3)^5

but this is not the correct answer, unless there's some algebra I'm not seeing with the answer above - I suspect I'm doing something amiss. Any help is appreciated!