how do 9-9 sin^2 x become 9(1-sin^2 x)

9-9 sin^2 x become 9(1-sin^2 x)

hopefully your are comfortable with this:

9-9y

= 9*1-9*y

=9(1-y)

I have factored out the 9    

Ok now lets look at yours

$$\\9-9 sin^2 x\\\\ =\textcolor[rgb]{0,0,1}{9}*1-\textcolor[rgb]{0,0,1}{9}*sin^2 x\\\\ =\textcolor[rgb]{0,0,1}{9}(1-sin^2 x) \textcolor[rgb]{0,0,1}{}$$

Again I have factored out the 9   :))