Algebra

There are 2 ways to do the problem. 

First, we could take a look at all the possible conbinations we could have to give us x^2. 

First off, we have 8x*x = 8x^2. 

Next, we have 7x*x=x^2

Lastly, we have x^2*1 = x^2

Adding all the coefficients up, we get $8+7+1=16$

We could also just factor it, which isn't reccomended, but we get

$x^{7}+4x^{6}+4x^{5}+19x^{4}+19x^{3}+16x^{2}+16x+1$

Which shows the coefficient of x^2 is 16. 

So our final answer is 16

Thanks! :)