Question 46534
Well, you did a lot of work but I don't think that you have actually anwered the question.

Let N be the number.
The number N, increased by 15 is just (N+15) and the number N, minus 8 is just (N-8)

The product of these two is:

(N+15)(N-8) ...and if you perform the indicated multiplication, you'll get:
{{{N^2 + 7N - 120}}}