Composite function: What am I doing wrong (pictures included)

Question

anonymous · Answer

attachment

anonymous · Answer

$$D(p)=\frac{ -p ^{2} }{ 207 }+400$$
$$p(c)=3c-18$$
^^Those are the two functions I need to make a composite function

anonymous · Answer

always make sure to use parenthesis

anonymous · Answer

Here is my work:
$$\frac{ -(3c-18)^{2} }{ 207 }+400$$
$$\frac{ -3(c-6)^{2} }{ 207 }+400$$
$$\frac{ -(c-6)^{2} }{ 69 }+400$$
$$\frac{ -c ^{2}+12c-36}{ 69 }+400$$

mertsj · Answer

$$\frac{-(3c-18)^2}{207}=\frac{-(9c^2-72c+324)}{207}=\frac{-9(c^2-8c+36)}{207}$$

anonymous · Answer

Ugh, yep. Yep.

mertsj · Answer

Sorry.  72 should be 108

anonymous · Answer

So I just need to square what I pull out? So I thought I needed to pull out a 3, but it's actually 3squared because of the square?

anonymous · Answer

Probably better for me if I just foil it out first.

mertsj · Answer

Remember the order of operations says powers first for a reason.  The entire quantity was to have been squared.  You removed a 3 which didn't get squared and that was the problem.

anonymous · Answer

Thank you, you're a life saver!