<s>[INST] Coefficent of an equation I am suppose to find the coefficent of x^2 in this equation

after doing the calculation I ended up with this

but that is the wrong answer what is that I am missing?
 [/INST] It is actually a bit less confusing (you don't have to expand the brackets with three terms)  if you write 
$$
f(f(x))=(x^2+bx+c)^2+b(x^2+bx+c)+c=(x^2+bx+c)(x^2+bx+c+(b+c))
=x^4+bx^3+(c+b)x^2+bx^3+b^2 x^2+b(c+b)x+cx^2+bcx+c(b+c)+c
$$
The it is clear tha the coefficient at $x^2$ is $c+b+b^2+c=2 \cdot 15 -23+23^2$
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